18
Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena Puninski Manchester, April 2018 1

Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

  • Upload
    others

  • View
    1

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Leavitt path algebras are Bézout

Alberto Tonolo, Università di Padova

Conference in memory of Gena PuninskiManchester, April 2018

�1

Page 2: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

The key dates for Leavitt path algebraslate ’50’s: Leavitt and non-IBN rings

mid ’60’s: Cohn and a class of algebras that “… may be regarded as pathological rings”

mid ’70’s: Bergman and the monoid-realization theorem

late ’70’s: Cuntz and graph C*-algebras

2005: Abrams and Aranda Pino 2007: Ara, Moreno and Pardo

Abrams, Ara, Siles Molina: Leavitt path algebras, Lecture Notes in Mathematics Vol. 2191, Springer Verlag, 2017.

Page 3: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

A graph and its extended graph

v1<latexit sha1_base64="8PAKmmixM9V7EuJjn4WJYmj2zAM=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">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</latexit>

v2<latexit sha1_base64="RnLauIjsfIi1c/EKrcB2wuxx9a8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">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</latexit>

v3<latexit sha1_base64="aCJXJ5RlxA9vJSXn+kHy1M4mML0=">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</latexit><latexit sha1_base64="7+An/e4ZjGTsSKaG/UAenbk8Nsc=">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</latexit><latexit sha1_base64="7+An/e4ZjGTsSKaG/UAenbk8Nsc=">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</latexit>

v4<latexit sha1_base64="5o7IKDY9gLFdRStvBpyGFyzmiOI=">AAADXXicvVJNb9NAEN0mUEoopS0HDlxWVJE4oMgOtWgOlSo+JI5FIbRSEkXj9ThZdXdt7Y5bIis/gSv8FY78DW78FNYxhaSCKyNZen4z82b37cS5ko6C4PtGo3nr9uadrbute9v3dx7s7u1/cFlhBQ5EpjJ7HoNDJQ0OSJLC89wi6FjhWXzxqsqfXaJ1MjPvaZ7jWMPUyFQKIE/1LyeHk92DoBNEvSgMeNCJgrD3vAK93tFhFPGwEyzj4GT/6+tvjLHTyV7jzSjJRKHRkFDg3DDs5jQuwZIUChetUeEwB3EBUxx6aECjG5fLsy542zMJTzPrP0N8ya52lKCdm+vYV2qgmbuZq8i/5YYFpUfjUpq8IDSiHpQWilPGq4vzRFoUpOYegLDSn5WLGVgQ5O1ptVfHTDHTSHa+fhUFJnECvIerBYQf6UomNDvm3SjIaU1pmHt7nuW+x9Y1YVea+n+Gcjqj4zCUZk3PosErkWntp5WjFLRU8wRTKBQtypFLr3Fb+EeWwBXURkrD+2Ac76OV6U0Z50l0f2Ti3zKtUZyppHKzXYH/+HYtv3jX28X/DQbdTq8TvPML+JLVscUesyfsKQvZC3bC3rJTNmCCTdkn9pl9afxobja3mzt1aWPjV89DthbNRz8BHA0cOw==</latexit><latexit sha1_base64="DY7vSTAraABkoaKhE1CBCXv4ZaE=">AAADXXicvVLNbtNAEN4mUIop/T1w4LKiioQQiuxQi+ZQqeJH4lgUQivFUbRej51Vd9fW7rglsvIIXOEZeAMegys3HoV1TCGp4MpIlj5/M/PN7rcTF1JY9P3va632rdvrdzbuevc2729t7+zuvbd5aTgMeS5zcx4zC1JoGKJACeeFAaZiCWfxxcs6f3YJxopcv8NZAWPFMi1SwRk6anA5OZzsHPhdP+yHgU/9bugH/Wc16PePDsOQBl1/EQcne19ffdv/8uR0stt6HSU5LxVo5JJZOwp6BY4rZlBwCXMvKi0UjF+wDEYOaqbAjqvFWee045iEprlxn0a6YJc7KqasnanYVSqGU3szV5N/y41KTI/GldBFiaB5MygtJcWc1heniTDAUc4cYNwId1bKp8wwjs4er7M8JoNcAZrZ6lUk04nlzHm4XIDwAa9EgtNj2gv9AleURoWz52nhekxTE/SEbv6nILIpHgeB0Ct6BjRc8VwpN62KUqaEnCWQslLivIpseo073D2yYFSyxkih6YBpSwdgRHpTxjoS7B+Z+LeMF8W5TGo3OzX4j2/nucW73i76bzDsdftd/61bwBekiQ3ykDwij0lAnpMT8oackiHhJCMfySfyufWjvd7ebG81pa21Xz37ZCXaD34CyVodMQ==</latexit><latexit sha1_base64="DY7vSTAraABkoaKhE1CBCXv4ZaE=">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</latexit>

v5<latexit sha1_base64="XEnGBwIhIUAc946elKahyxHOr10=">AAADXXicvVJNb9NAEN0mUEoopS0HDlxWVJE4oMhOsWgOlSo+JI5FIbRSEkXj9ThZdXdt7Y5bIis/gSv8FY78DW78FNYxhaSCKyNZen4z82b37cS5ko6C4PtGo3nr9uadrbute9v3dx7s7u1/cFlhBQ5EpjJ7HoNDJQ0OSJLC89wi6FjhWXzxqsqfXaJ1MjPvaZ7jWMPUyFQKIE/1LyfRZPcg6ARRLwoDHnSiIOwdVqDXO3oeRTzsBMs4ONn/+vobY+x0std4M0oyUWg0JBQ4Nwy7OY1LsCSFwkVrVDjMQVzAFIceGtDoxuXyrAve9kzC08z6zxBfsqsdJWjn5jr2lRpo5m7mKvJvuWFB6dG4lCYvCI2oB6WF4pTx6uI8kRYFqbkHIKz0Z+ViBhYEeXta7dUxU8w0kp2vX0WBSZwA7+FqAeFHupIJzY55NwpyWlMa5t6eZ7nvsXVN2JWm/p+hnM7oOAylWdOzaPBKZFr7aeUoBS3VPMEUCkWLcuTSa9wW/pElcAW1kdLwPhjH+2hlelPGeRLdH5n4t0xrFGcqqdxsV+A/vl3LL971dvF/g0G30+sE7/wCvmR1bLHH7Al7ykL2gp2wt+yUDZhgU/aJfWZfGj+am83t5k5d2tj41fOQrUXz0U8fBBw8</latexit><latexit sha1_base64="yaUbGn+TXLSwb/L1QU3Kk9yCgMc=">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</latexit><latexit sha1_base64="yaUbGn+TXLSwb/L1QU3Kk9yCgMc=">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</latexit>

v6<latexit sha1_base64="UfomTyGXDzzJ10RXwIfU4GSYSXE=">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</latexit><latexit sha1_base64="3gg7qt9+5vGUIG1FQwwKinA/wxc=">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</latexit><latexit sha1_base64="3gg7qt9+5vGUIG1FQwwKinA/wxc=">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</latexit>

v!<latexit sha1_base64="+ESNGFHMjPIRmpA5ljhoZ8TRV7k=">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</latexit><latexit sha1_base64="hJARN2wzcpXVoo8WRz9Wipj7Gqc=">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</latexit><latexit sha1_base64="hJARN2wzcpXVoo8WRz9Wipj7Gqc=">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</latexit>

e2<latexit sha1_base64="+qvft35mNCYBd7mHkko9V+wUF/c=">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</latexit><latexit sha1_base64="4TWgrdRvjtxoRH9cYpisFS/0ZOc=">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</latexit><latexit sha1_base64="4TWgrdRvjtxoRH9cYpisFS/0ZOc=">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</latexit>

e1<latexit sha1_base64="Gahtq2xaFc9C2zq3tCEmh3z/KjE=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">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</latexit>

e3<latexit sha1_base64="u6aps99kjMZnFt6LACGZVHxr8GA=">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</latexit><latexit sha1_base64="ko+763tzlQVosGPwibi3OupeYmY=">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</latexit><latexit sha1_base64="ko+763tzlQVosGPwibi3OupeYmY=">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</latexit>

e4<latexit sha1_base64="u2R2RalfWEo8fhoEzg7jafnylrE=">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</latexit><latexit sha1_base64="qjGof5nbXTi2LG7wMGqXhXEqGtw=">AAADXXicvVLBbhMxEHUTKCGU0sKBAxeLKhIHFK0joMmhUiWEhMSlKIRWSqJo1jubWLW9K3uWEq36CVzhP/iWXrjxE9zxdikkFVwZaaW3b2be2M8T51p5iqJvG43mjZubt1q323e27m7f29m9/95nhZM4kpnO3EkMHrWyOCJFGk9yh2Bijcfx6csqf/wBnVeZfUfLHKcG5lalSgIFaoizZ7OdvagbRZEQgldA7L+IAhgM+j3R56JKhdg7bP34enHReHM02228miSZLAxakhq8H4teTtMSHCmp8bw9KTzmIE9hjuMALRj00/LyrOe8E5iEp5kLnyV+ya52lGC8X5o4VBqghb+eq8i/5cYFpf1pqWxeEFpZD0oLzSnj1cV5ohxK0ssAQDoVzsrlAhxICva0O6tj5pgZJLdcv4oGm3gJwcPVAsKPdKYSWhzw3vMopzWlcR7seZqHHlfXiJ6y9f8C1XxBB0Iou6bn0OKZzIwJ08pJCkbpZYIpFJrOy4lPr3BHhkdWwDXURirLh2A9H6JT6XUZH0j0f2Ti3zLtSZzppHKzU4H/+HbtsHhX28X/DUa97qAbvQ0L2Gd1tNgj9pg9YYLts0P2mh2xEZNszj6xz+xL43tzs7nV3K5LGxu/eh6wtWg+/AnAYh3e</latexit><latexit sha1_base64="qjGof5nbXTi2LG7wMGqXhXEqGtw=">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</latexit>

e5<latexit sha1_base64="2oTVAYPOXK7qVoTAKdaZt9kQovk=">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</latexit><latexit sha1_base64="fuQ1sFb76il7pyt7uv1eo8bJJpg=">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</latexit><latexit sha1_base64="fuQ1sFb76il7pyt7uv1eo8bJJpg=">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</latexit>

e6<latexit sha1_base64="4hpldoBTI3TdciTk2lw/afLqBL4=">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</latexit><latexit sha1_base64="XK6KnUlmY1y/hiZoiu7q7bTAgSU=">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</latexit><latexit sha1_base64="XK6KnUlmY1y/hiZoiu7q7bTAgSU=">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</latexit>

e7<latexit sha1_base64="ZikDrdAbsc1p8mE1uoX8u32g7fg=">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</latexit><latexit sha1_base64="DItlr6l1+XJLuVwmgc5P4ZU9qUE=">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</latexit><latexit sha1_base64="DItlr6l1+XJLuVwmgc5P4ZU9qUE=">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</latexit>e8

<latexit sha1_base64="lycQNS7HDk/TwRHKTdDQ/1kZ1bI=">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</latexit><latexit sha1_base64="I4p7JkHKI5C2HUX4sU7SwGQkrL4=">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</latexit><latexit sha1_base64="I4p7JkHKI5C2HUX4sU7SwGQkrL4=">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</latexit>

e!<latexit sha1_base64="miKXffsTgVs7S3sc7Y2C7OV8gB8=">AAADYnicvVLNbhMxEHYTfkLKTwNHOFhUkTigaDcSNDlUqoSQOBaV0EjZKJr1ziZWbe/Knm0brfISXOEpeAJegwfgEbjj7TaQVHBlJEvf/H1jf544V9JREHzfaTRv3b5zt3WvvXv/wcNHe53HH11WWIEjkanMjmNwqKTBEUlSOM4tgo4VnsZnb6r86TlaJzPzgZY5TjXMjUylAPKhMc6iTOMcZnv7QS8IgjAMeQXCg9eBB8PhoB8OeFilvO0ftX5+/cYYO551Gm+jJBOFRkNCgXOTsJ/TtARLUihctaPCYQ7iDOY48dCARjctry684l0fSXiaWX8M8avoZkcJ2rmljn2lBlq4m7kq+LfcpKB0MC2lyQtCI+pBaaE4Zbx6PU+kRUFq6QEIK/1duViABUFeo3Z3c8wcvTJkl9tPUWASJ8ALuVlAeEkXMqHFIe+/CnLaYprkXp6Xue+xdU3Yl6b2FyjnCzoMQ2m2+CwavBCZ1n5aGaWgpVommEKhaFVGLl3jrvA/LYErqIWUhp+AcfwErUxv0jgfRPeHJv5N047iTCWVmt0K/Me/a/vFW28X/zcY9XvDXvDeL+CA1dZiT9lz9oKF7IAdsXfsmI2YYIp9Yp/Zl8aP5m6z03xSlzZ2rnuu/bU1n/0CrEYfDA==</latexit><latexit sha1_base64="KP/aQ8GcDmkMYALYuvJ6yN27yLs=">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</latexit><latexit sha1_base64="KP/aQ8GcDmkMYALYuvJ6yN27yLs=">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</latexit>

e⇤1

<latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">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</latexit><latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">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</latexit><latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">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</latexit><latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">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</latexit>

e⇤2

<latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit><latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit><latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit><latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit>

e⇤3

<latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">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</latexit><latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">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</latexit><latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">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</latexit><latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">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</latexit>

e⇤4

<latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">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</latexit><latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">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</latexit><latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">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</latexit><latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">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</latexit>

e⇤5

<latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit><latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit><latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit><latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit>

e⇤6

<latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit><latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit><latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit><latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit>

e⇤7

<latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">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</latexit><latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">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</latexit><latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">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</latexit><latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">AAADX3icvVJdb9MwFPVaPkqArYMnxItFVQkhVCWhrN3DpEkIicehUTapKZXj3LTWbCeybxhR1N/AK/w0XvklOEsH7QSvXMnS8bmfPr5xLoVF3/+x02rfun3nbueed//Bw9297v6jjzYrDIcJz2RmzmNmQQoNExQo4Tw3wFQs4Sy+eFP7zz6DsSLTH7DMYabYQotUcIaOmsB89OnFvNvzB4fjg3B4QP2B74+CMKhBOBq+GtLAMbX1yNpO5vutt1GS8UKBRi6ZtdMgzHFWMYOCS1h5UWEhZ/yCLWDqoGYK7Ky6mnZF+45JaJoZdzTSK3Yzo2LK2lLFLlIxXNqbvpr8m29aYDqeVULnBYLmTaO0kBQzWj+dJsIAR1k6wLgRblbKl8wwjk6grS4LyBSgKVdef7OBZDqxnDkVNyIihC94KRJcHtHwtZ/jdk7u5HmZuxzTxASh0M19CWKxxKMgEHqrngENlzxTynWropQpIcsEUlZIXFWRTa9xn7tvFoxK1ggpND1l2tJTMCK9WcY6EuyfMvHvMl4UZzKp1ezX4D/+necW73q76L/BJBwcDoL3fu94vN7ADnlKnpHnJCAjckzekRMyIZwI8pV8I99bP9ud9m6724S2dtY5j8mWtZ/8AvXBGqY=</latexit>

e⇤8

<latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">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</latexit><latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">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</latexit><latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">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</latexit><latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">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</latexit>

e⇤!

<latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">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</latexit><latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">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</latexit><latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">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</latexit><latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">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</latexit>

e1 7! v1<latexit sha1_base64="DdTxMJwbXkrMo8+QuHRMr+7ON3w=">AAADaHicvVLdahNBFJ4m/tT400YvRLwZGgJeSNgNiPaiUBTBy0qNLWRjODt7Njt0ZnaZOdt2WfIe3upb+Qy+hJNs1CT12gMD33znd745caGkoyD4sdNq37p95+7uvc79Bw8f7e13H392eWkFjkSucnseg0MlDY5IksLzwiLoWOFZfPFu4T+7ROtkbj5RVeBEw8zIVAogT33BaRhpKBzl/HIaTvd7wSBYGr8JwhXosZWdTLut91GSi1KjIaHAuXE4LGhSgyUpFM47UemwAHEBMxx7aECjm9TLsee875mEp7n1xxBfsusZNWjnKh37SA2UuW3fgvyXb1xS+mZSS1OUhEY0jdJScf/KhQY8kRYFqcoDEFb6WbnIwIIgr9RGlxnmGslW805/vYECkzgBXs61iIjwmq5kQtkRH74KCtrMKbw8LwufY5uYcChNc89QzjI6CkNpNupZNHglcq19tzpKQUtVJZhCqWheRy79jfvC/7cErqARUhp+CsbxU7Qy3S7jPInub5n4T5lOFOcqWajZX4D/+Hcdv3jh9prdBKPh4HAQfgx6x29XG7jLnrMD9oKF7DU7Zh/YCRsxwSz7yr6x762f7W77aftZE9raWeU8YRvWPvgFKa4eUA==</latexit><latexit sha1_base64="DdTxMJwbXkrMo8+QuHRMr+7ON3w=">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</latexit><latexit sha1_base64="DdTxMJwbXkrMo8+QuHRMr+7ON3w=">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</latexit><latexit sha1_base64="DdTxMJwbXkrMo8+QuHRMr+7ON3w=">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</latexit>

e1 7! v2<latexit sha1_base64="JcmbmDPM6loz7tJlK6tkwFiK1JQ=">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</latexit><latexit sha1_base64="JcmbmDPM6loz7tJlK6tkwFiK1JQ=">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</latexit><latexit sha1_base64="JcmbmDPM6loz7tJlK6tkwFiK1JQ=">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</latexit><latexit sha1_base64="JcmbmDPM6loz7tJlK6tkwFiK1JQ=">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</latexit>

bE = (E0, E1 [ E1⇤, s, r)<latexit sha1_base64="OAmmZ9pp/WneZfQW5OOcfyWYzMI=">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</latexit><latexit sha1_base64="OAmmZ9pp/WneZfQW5OOcfyWYzMI=">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</latexit><latexit sha1_base64="OAmmZ9pp/WneZfQW5OOcfyWYzMI=">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</latexit><latexit sha1_base64="OAmmZ9pp/WneZfQW5OOcfyWYzMI=">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</latexit>

E = (E0, E1, s, r)<latexit sha1_base64="Y8c1YS6ipsmxydXm3Z6cHb4OSaI=">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</latexit><latexit sha1_base64="Y8c1YS6ipsmxydXm3Z6cHb4OSaI=">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</latexit><latexit sha1_base64="Y8c1YS6ipsmxydXm3Z6cHb4OSaI=">AAAEO3icvZJLj9MwEMfdDY+lPLYLRy4WVaVFqio7S2hzqLQCVeK4aCm7UlMqx3Faq44T2Q5LFeWr8T04ceGEuHLHTQv0AQcujBTpn/FvHpqZMBNcG4Q+1Q6cGzdv3T68U7977/6Do8bxw7c6zRVlQ5qKVF2FRDPBJRsabgS7yhQjSSjYZTh/uXy/fM+U5ql8YxYZGydkKnnMKTHWNWl8LoIqyUhNw3GBOn7P8057bdRByHf9rhW+7+MuLgdl/2SHRZ7vYWQRD2H/FFVs75nnlYN3qGzDXRohjHGVGXefr2kX9yyN9+m/9qH/gVXl00mjWZW2BvcFXosmWNv55PhgEEQpzRMmDRVE6xF2MzMuiDKcClbWg1yzjNA5mbKRlZIkTI+LqqEStqwngnGq7CcNrLybEQVJtF4koSUTYmZ6923p/NPbKDdxb1xwmeWGSboqFOcCmhQu1wojrhg1YmEFoYrbXiGdEUWoscvfqjJlacKMWpT11mYBQWSkKbEXskEEhn0w1zwysz50PZSZ7ZjMjqed2Ri1YrDL5ep/xvh0ZvoYc7mVTzHJrmmaJLZaEcQk4WIRsZjkwpRFoOOfukXtCXMCBVkNkkt4QaSGF0zxeDeNtk6mf6cJf6WpB2EqouU0W0vxH3dXt4eHd89sXwzdjt/Br1Hz7MX6Ag/BY/AEnAAMuuAMvALnYAhobVCb10wtdz46X5yvzrcVelBbxzwCW+Z8/wHrIFqL</latexit><latexit sha1_base64="Y8c1YS6ipsmxydXm3Z6cHb4OSaI=">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</latexit>

s : E1 ! E0<latexit sha1_base64="tJ40fFIAzfaFs/OV5vT5HotrHCM=">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</latexit><latexit sha1_base64="tJ40fFIAzfaFs/OV5vT5HotrHCM=">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</latexit><latexit sha1_base64="tJ40fFIAzfaFs/OV5vT5HotrHCM=">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</latexit><latexit sha1_base64="tJ40fFIAzfaFs/OV5vT5HotrHCM=">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</latexit>

r : E1 ! E0<latexit sha1_base64="HONdh5uk0UAwtSRpwq/wqukxyTI=">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</latexit><latexit sha1_base64="HONdh5uk0UAwtSRpwq/wqukxyTI=">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</latexit><latexit sha1_base64="HONdh5uk0UAwtSRpwq/wqukxyTI=">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</latexit><latexit sha1_base64="HONdh5uk0UAwtSRpwq/wqukxyTI=">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</latexit>

Page 4: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Leavitt path algebras

e5<latexit sha1_base64="2oTVAYPOXK7qVoTAKdaZt9kQovk=">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</latexit><latexit sha1_base64="fuQ1sFb76il7pyt7uv1eo8bJJpg=">AAADXXicvVLBbhMxEHUTKCGU0sKBAxeLKhIHFK0jlSaHSpUQEhKXohBaKYmiWe9sYtX2ruxZSrTKJ3CF/+BbeuHGT3DH26XQVHBlpJXevpl5Yz9PnGvlKYq+bTSat25v3mndbd/bur/9YGf34XufFU7iSGY6c6cxeNTK4ogUaTzNHYKJNZ7EZy+r/MkHdF5l9h0tc5wamFuVKgkUqCHO9mc7e1E3iiIhBK+AOHgRBTAY9Huiz0WVCrF31Prx9eKi8eZ4ttt4NUkyWRi0JDV4Pxa9nKYlOFJS46o9KTzmIM9gjuMALRj00/LyrCveCUzC08yFzxK/ZK93lGC8X5o4VBqghb+Zq8i/5cYFpf1pqWxeEFpZD0oLzSnj1cV5ohxK0ssAQDoVzsrlAhxICva0O9fHzDEzSG65fhUNNvESgofXCwg/0rlKaHHIe/tRTmtK4zzY8zwPPa6uET1l6/8FqvmCDoVQdk3PocVzmRkTppWTFIzSywRTKDStyolPr3BHhkdWwDXURirLh2A9H6JT6U0ZH0j0f2Ti3zLtSZzppHKzU4H/+HbtsHhX28X/DUa97qAbvQ0L2Gd1tNgT9pQ9Y4IdsCP2mh2zEZNszj6xz+xL43tzs7nV3K5LGxu/eh6xtWg+/gnDWR3f</latexit><latexit sha1_base64="fuQ1sFb76il7pyt7uv1eo8bJJpg=">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</latexit>

e!<latexit sha1_base64="miKXffsTgVs7S3sc7Y2C7OV8gB8=">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</latexit><latexit sha1_base64="KP/aQ8GcDmkMYALYuvJ6yN27yLs=">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</latexit><latexit sha1_base64="KP/aQ8GcDmkMYALYuvJ6yN27yLs=">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</latexit>

v!<latexit sha1_base64="+ESNGFHMjPIRmpA5ljhoZ8TRV7k=">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</latexit><latexit sha1_base64="hJARN2wzcpXVoo8WRz9Wipj7Gqc=">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</latexit><latexit sha1_base64="hJARN2wzcpXVoo8WRz9Wipj7Gqc=">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</latexit>

v1<latexit sha1_base64="8PAKmmixM9V7EuJjn4WJYmj2zAM=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">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</latexit>

v2<latexit sha1_base64="RnLauIjsfIi1c/EKrcB2wuxx9a8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">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</latexit>

v3<latexit sha1_base64="aCJXJ5RlxA9vJSXn+kHy1M4mML0=">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</latexit><latexit sha1_base64="7+An/e4ZjGTsSKaG/UAenbk8Nsc=">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</latexit><latexit sha1_base64="7+An/e4ZjGTsSKaG/UAenbk8Nsc=">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</latexit>

v4<latexit sha1_base64="5o7IKDY9gLFdRStvBpyGFyzmiOI=">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</latexit><latexit sha1_base64="DY7vSTAraABkoaKhE1CBCXv4ZaE=">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</latexit><latexit sha1_base64="DY7vSTAraABkoaKhE1CBCXv4ZaE=">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</latexit>

v5<latexit sha1_base64="XEnGBwIhIUAc946elKahyxHOr10=">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</latexit><latexit sha1_base64="yaUbGn+TXLSwb/L1QU3Kk9yCgMc=">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</latexit><latexit sha1_base64="yaUbGn+TXLSwb/L1QU3Kk9yCgMc=">AAADXXicvVLNbtNAEN4mUEoopT8HDlxWVJEQQpEdsGgOlSp+JI5FIbRSEkXj9ThZdXdt7Y5bIquPwBWegTfgMbhy41FYxxSSCq6MZOnzNzPf7H47ca6koyD4vtZo3ri5fmvjduvO5t2te9s7u+9dVliBA5GpzJ7G4FBJgwOSpPA0twg6VngSn72s8ifnaJ3MzDua5zjWMDUylQLIU/3zSTTZ3g86QdSLwoAHnSgIe08r0OsdPIsiHnaCRewf7X599W3vy+PjyU7j9SjJRKHRkFDg3DDs5jQuwZIUCi9bo8JhDuIMpjj00IBGNy4XZ73kbc8kPM2s/wzxBbvcUYJ2bq5jX6mBZu56riL/lhsWlB6MS2nygtCIelBaKE4Zry7OE2lRkJp7AMJKf1YuZmBBkLen1V4eM8VMI9n56lUUmMQJ8B4uFxB+oAuZ0OyQd6MgpxWlYe7teZL7HlvXhF1p6v8ZyumMDsNQmhU9iwYvRKa1n1aOUtBSzRNMoVB0WY5ceoXbwj+yBK6gNlIa3gfjeB+tTK/LOE+i+yMT/5ZpjeJMJZWb7Qr8x7dr+cW72i7+bzDodnqd4K1fwBesjg32gD1kj1jInrMj9oYdswETbMo+sk/sc+NHc7252dyqSxtrv3r22Eo07/8EzFEdMg==</latexit>

v6<latexit sha1_base64="UfomTyGXDzzJ10RXwIfU4GSYSXE=">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</latexit><latexit sha1_base64="3gg7qt9+5vGUIG1FQwwKinA/wxc=">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</latexit><latexit sha1_base64="3gg7qt9+5vGUIG1FQwwKinA/wxc=">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</latexit>

e2<latexit sha1_base64="+qvft35mNCYBd7mHkko9V+wUF/c=">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</latexit><latexit sha1_base64="4TWgrdRvjtxoRH9cYpisFS/0ZOc=">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</latexit><latexit sha1_base64="4TWgrdRvjtxoRH9cYpisFS/0ZOc=">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</latexit>

e1<latexit sha1_base64="Gahtq2xaFc9C2zq3tCEmh3z/KjE=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">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</latexit>

e3<latexit sha1_base64="u6aps99kjMZnFt6LACGZVHxr8GA=">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</latexit><latexit sha1_base64="ko+763tzlQVosGPwibi3OupeYmY=">AAADXXicvVLBbhMxEHUTKCGU0sKBAxeLKhIHFK2DoMmhUiWEhMSlKIRWSqJo1jubWLW9K3uWEq36CVzhP/iWXrjxE9zxdikkFVwZaaW3b2be2M8T51p5iqJvG43mjZubt1q323e27m7f29m9/95nhZM4kpnO3EkMHrWyOCJFGk9yh2Bijcfx6csqf/wBnVeZfUfLHKcG5lalSgIFaoizZ7OdvagbRZEQgldA7L+IAhgM+j3R56JKhdg7bP34enHReHM02228miSZLAxakhq8H4teTtMSHCmp8bw9KTzmIE9hjuMALRj00/LyrOe8E5iEp5kLnyV+ya52lGC8X5o4VBqghb+eq8i/5cYFpf1pqWxeEFpZD0oLzSnj1cV5ohxK0ssAQDoVzsrlAhxICva0O6tj5pgZJLdcv4oGm3gJwcPVAsKPdKYSWhzw3vMopzWlcR7seZqHHlfXiJ6y9f8C1XxBB0Iou6bn0OKZzIwJ08pJCkbpZYIpFJrOy4lPr3BHhkdWwDXURirLh2A9H6JT6XUZH0j0f2Ti3zLtSZzppHKzU4H/+HbtsHhX28X/DUa97qAbvQ0L2Gd1tNgj9pg9YYLts0P2mh2xEZNszj6xz+xL43tzs7nV3K5LGxu/eh6wtWg+/Am9ax3d</latexit><latexit sha1_base64="ko+763tzlQVosGPwibi3OupeYmY=">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</latexit>

e4<latexit sha1_base64="u2R2RalfWEo8fhoEzg7jafnylrE=">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</latexit><latexit sha1_base64="qjGof5nbXTi2LG7wMGqXhXEqGtw=">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</latexit><latexit sha1_base64="qjGof5nbXTi2LG7wMGqXhXEqGtw=">AAADXXicvVLBbhMxEHUTKCGU0sKBAxeLKhIHFK0joMmhUiWEhMSlKIRWSqJo1jubWLW9K3uWEq36CVzhP/iWXrjxE9zxdikkFVwZaaW3b2be2M8T51p5iqJvG43mjZubt1q323e27m7f29m9/95nhZM4kpnO3EkMHrWyOCJFGk9yh2Bijcfx6csqf/wBnVeZfUfLHKcG5lalSgIFaoizZ7OdvagbRZEQgldA7L+IAhgM+j3R56JKhdg7bP34enHReHM02228miSZLAxakhq8H4teTtMSHCmp8bw9KTzmIE9hjuMALRj00/LyrOe8E5iEp5kLnyV+ya52lGC8X5o4VBqghb+eq8i/5cYFpf1pqWxeEFpZD0oLzSnj1cV5ohxK0ssAQDoVzsrlAhxICva0O6tj5pgZJLdcv4oGm3gJwcPVAsKPdKYSWhzw3vMopzWlcR7seZqHHlfXiJ6y9f8C1XxBB0Iou6bn0OKZzIwJ08pJCkbpZYIpFJrOy4lPr3BHhkdWwDXURirLh2A9H6JT6XUZH0j0f2Ti3zLtSZzppHKzU4H/+HbtsHhX28X/DUa97qAbvQ0L2Gd1tNgj9pg9YYLts0P2mh2xEZNszj6xz+xL43tzs7nV3K5LGxu/eh6wtWg+/AnAYh3e</latexit>

e6<latexit sha1_base64="4hpldoBTI3TdciTk2lw/afLqBL4=">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</latexit><latexit sha1_base64="XK6KnUlmY1y/hiZoiu7q7bTAgSU=">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</latexit><latexit sha1_base64="XK6KnUlmY1y/hiZoiu7q7bTAgSU=">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</latexit>

e7<latexit sha1_base64="ZikDrdAbsc1p8mE1uoX8u32g7fg=">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</latexit><latexit sha1_base64="DItlr6l1+XJLuVwmgc5P4ZU9qUE=">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</latexit><latexit sha1_base64="DItlr6l1+XJLuVwmgc5P4ZU9qUE=">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</latexit>e8

<latexit sha1_base64="lycQNS7HDk/TwRHKTdDQ/1kZ1bI=">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</latexit><latexit sha1_base64="I4p7JkHKI5C2HUX4sU7SwGQkrL4=">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</latexit><latexit sha1_base64="I4p7JkHKI5C2HUX4sU7SwGQkrL4=">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</latexit>

e⇤1

<latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">AAADX3icvVJdb9MwFPVaPkqArYMnxItFVQkhVCWhrN3DpEkIicehUTapKZXj3LTWbCeybxhR1N/AK/w0XvklOEsH7QSvXMnS8bmfPr5xLoVF3/+x02rfun3nbueed//Bw9297v6jjzYrDIcJz2RmzmNmQQoNExQo4Tw3wFQs4Sy+eFP7zz6DsSLTH7DMYabYQotUcIaOmsA8+PRi3u35g8PxQTg8oP7A90dBGNQgHA1fDWngmNp6ZG0n8/3W2yjJeKFAI5fM2mkQ5jirmEHBJay8qLCQM37BFjB1UDMFdlZdTbuifcckNM2MOxrpFbuZUTFlbaliF6kYLu1NX03+zTctMB3PKqHzAkHzplFaSIoZrZ9OE2GAoywdYNwINyvlS2YYRyfQVpcFZArQlCuvv9lAMp1YzpyKGxERwhe8FAkuj2j42s9xOyd38rzMXY5pYoJQ6Oa+BLFY4lEQCL1Vz4CGS54p5bpVUcqUkGUCKSskrqrIpte4z903C0Yla4QUmp4ybekpGJHeLGMdCfZPmfh3GS+KM5nUavZr8B//znOLd71d9N9gEg4OB8F7v3c8Xm9ghzwlz8hzEpAROSbvyAmZEE4E+Uq+ke+tn+1Oe7fdbUJbO+ucx2TL2k9+AePrGqA=</latexit><latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">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</latexit><latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">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</latexit><latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">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</latexit>

e⇤2

<latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit><latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit><latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit><latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit>

e⇤3

<latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">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</latexit><latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">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</latexit><latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">AAADX3icvVJdb9MwFPVaPkqA0cET4sWiqoQQqpKsrN3DpEkIicehUTapKZXj3DTWbCeybxhR1N/AK/w0XvklOGsH7QSvXMnS8bmfPr5xIYVF3/+x02rfun3nbueed//Bw91H3b3HH21eGg4TnsvcnMfMghQaJihQwnlhgKlYwll88abxn30GY0WuP2BVwEyxhRap4AwdNYH5/qeX827PHxyOD8LhAfUHvj8KwqAB4Wi4P6SBYxrrkbWdzPdab6Mk56UCjVwya6dBWOCsZgYFl7D0otJCwfgFW8DUQc0U2Fl9Ne2S9h2T0DQ37mikV+xmRs2UtZWKXaRimNmbvob8m29aYjqe1UIXJYLmq0ZpKSnmtHk6TYQBjrJygHEj3KyUZ8wwjk6grS4LyBWgqZZef7OBZDqxnDkVNyIihC94KRLMjmj42i9wO6dw8rwqXI5ZxQSh0Kt7BmKR4VEQCL1Vz4CGS54r5brVUcqUkFUCKSslLuvIpte4z903C0YlWwkpND1l2tJTMCK9WcY6EuyfMvHvMl4U5zJp1Ow34D/+necW73q76L/BJBwcDoL3fu94vN7ADnlGnpMXJCAjckzekRMyIZwI8pV8I99bP9ud9m67uwpt7axznpAtaz/9BendGqI=</latexit><latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">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</latexit>

e⇤4

<latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">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</latexit><latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">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</latexit><latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">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</latexit><latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">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</latexit>

e⇤5

<latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit><latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit><latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit><latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit>

e⇤6

<latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit><latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit><latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit><latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit>

e⇤7

<latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">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</latexit><latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">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</latexit><latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">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</latexit><latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">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</latexit>

e⇤8

<latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">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</latexit><latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">AAADX3icvVJdb9MwFPVaPkqArYMnxItFVQkhVCWhrN3DpEkIicehUTapKZXj3LTWbCeybxhR1N/AK/w0XvklOEsH7QSvXMnS8bmfPr5xLoVF3/+x02rfun3nbueed//Bw9297v6jjzYrDIcJz2RmzmNmQQoNExQo4Tw3wFQs4Sy+eFP7zz6DsSLTH7DMYabYQotUcIaOmsB8/OnFvNvzB4fjg3B4QP2B74+CMKhBOBq+GtLAMbX1yNpO5vutt1GS8UKBRi6ZtdMgzHFWMYOCS1h5UWEhZ/yCLWDqoGYK7Ky6mnZF+45JaJoZdzTSK3Yzo2LK2lLFLlIxXNqbvpr8m29aYDqeVULnBYLmTaO0kBQzWj+dJsIAR1k6wLgRblbKl8wwjk6grS4LyBSgKVdef7OBZDqxnDkVNyIihC94KRJcHtHwtZ/jdk7u5HmZuxzTxASh0M19CWKxxKMgEHqrngENlzxTynWropQpIcsEUlZIXFWRTa9xn7tvFoxK1ggpND1l2tJTMCK9WcY6EuyfMvHvMl4UZzKp1ezX4D/+necW73q76L/BJBwcDoL3fu94vN7ADnlKnpHnJCAjckzekRMyIZwI8pV8I99bP9ud9m6724S2dtY5j8mWtZ/8Avi6Gqc=</latexit><latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">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</latexit><latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">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</latexit>

e⇤!

<latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">AAADZHicvVLdahNBFJ4m/tRotbV4JchgCIhI2F1jk14UCiJ4WamxxWwsZ2fPJkNnZpeZs9aw5C281ffyCXwNZ5tUk6K3Hhj45ju/881JCiUdBcGPjUbzxs1btzfvtO7e27r/YHvn4QeXl1bgUOQqt6cJOFTS4JAkKTwtLIJOFJ4k569r/8lntE7m5j3NChxrmBiZSQHkqY94FucaJ/Dp+dl2O+juD/ai3h4PukHQD6OwBlG/97LHQ8/U1mZLOzrbabyJ01yUGg0JBc6NwqigcQWWpFA4b8WlwwLEOUxw5KEBjW5cXY485x3PpDzLrT+G+CW7mlGBdm6mEx+pgabuuq8m/+YblZQNxpU0RUloxKJRVipOOa/fz1NpUZCaeQDCSj8rF1OwIMirtNZlgl4asrN5q7PaQIFJnQAv5UpETPiFLmRK0wMevQoKWs8pvDwvCp9jFzFhJM3iPkU5mdJBGEqzVs+iwQuRa+27VXEGWqpZihmUiuZV7LIr3BH+ryVwBQshpeHHYBw/Riuz62WcJ9H9KZP8LtOKk1yltZqdGvzHv2v5xbvaLv5vMIy6+93wXdA+HCw3cJM9Zk/ZMxayPjtkb9kRGzLBDPvKvrHvjZ/NreZu89EitLGxzNlla9Z88gs6uh0G</latexit><latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">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</latexit><latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">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</latexit><latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">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</latexit>

e⇤e0 = �e,e0r(e)<latexit sha1_base64="cx7nyQvBSwIFjivUSm18BZ8ic9U=">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</latexit><latexit sha1_base64="cx7nyQvBSwIFjivUSm18BZ8ic9U=">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</latexit><latexit sha1_base64="cx7nyQvBSwIFjivUSm18BZ8ic9U=">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</latexit><latexit sha1_base64="cx7nyQvBSwIFjivUSm18BZ8ic9U=">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</latexit>

vv0 = �v,v0v<latexit sha1_base64="2H38IGjJw3hQXqFZPMzGDURFFbA=">AAAEEnicvVJNb9NAEF3HfJTw0RSOcFgRReUQRXbAojlEqoqQkOBQVEIrxVG0Xo+TVXfX1u46JbL8M/grXDghrvwB/g3rJECScsiJkSw9v3nzZjUzUcaZNp7306m5N27eur13p3733v0H+42Dhx91misKA5ryVF1ERANnEgaGGQ4XmQIiIg7n0eWrKn8+A6VZKj+YeQYjQSaSJYwSY6lx40sRLkyGahKNCq/jBb3A99peJ/D83vMK9HpHL4KgnM0Oy34YAzdkXOxcVLZ3lh6W5e6240bT5heBrwN/BZpoFafjg9rrME5pLkAayonWQ7+bmVFBlGGUQ1kPcw0ZoZdkAkMLJRGgR8XiPSVuWSbGSarsJw1esOsVBRFaz0VklYKYqd7OVeS/csPcJEejgsksNyDpslGSc2xSXG0Lx0wBNXxuAaGK2bdiOiWKUGN3utFlAqkAo+ZlvbXegBMZa0rs4tcUoYFP5orFZtrH3cDLzGZNZsfTzmyNWmr8LpPL/ymwydT0fZ/JDT8FEq5oKoTtVoQJEYzPY0hIzo1dqk5+4xa1l8kI5mQ5SCbxGZEan4FiybaNtiTovzbRH5t6GKU8rqbZqsB/3F3dHp6/fWbXwaDb6XX8917z+GR1gXvoMXqKniEfvUTH6A06RQNEnSfOifPWeed+dr+639zvS2nNWdU8Qhvh/vgFJKFPxQ==</latexit><latexit sha1_base64="2H38IGjJw3hQXqFZPMzGDURFFbA=">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</latexit><latexit sha1_base64="2H38IGjJw3hQXqFZPMzGDURFFbA=">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</latexit><latexit sha1_base64="2H38IGjJw3hQXqFZPMzGDURFFbA=">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</latexit>

v =X

{e:s(e)=v}ee⇤

<latexit sha1_base64="31yzsdrJZaECvLaNQfvzLMTBcDc=">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</latexit><latexit sha1_base64="31yzsdrJZaECvLaNQfvzLMTBcDc=">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</latexit><latexit sha1_base64="31yzsdrJZaECvLaNQfvzLMTBcDc=">AAAElXicvVNNb9NAELVLgBK+WrggcbGoIhVURV4nbmKkoIovcaOohFaKQ7Rej5NV12trd90SWftb+DVc4cy/Ye0EaFIOPbGSpbcz770ZzY6jnFGpXPenvXGtcf3Gzc1bzdt37t67v7X94JPMCkFgSDKWiZMIS2CUw1BRxeAkF4DTiMFxdPqqyh+fgZA04x/VPIdxiqecJpRgZUKTbbtfhrXLSEyjcem2XT/wkbvntn0XBZ0KBEG/6/v6TA9CWaSTMizXJa6LENqrAOrtLyUe6mvQz9eoQd/3O/2aGnhBr6YGqIe01LtXd306uHrTodZXN77U7b7X3a+ZPeTVEq/X7XQ1fH6mJ1s7tZc5zmWAlmDHWp7DyfbGmzDOSJECV4RhKUfIy9W4xEJRwkA3w0JCjskpnsLIQI5TkOOy7kg7LROJnSQT5uPKqaMXFSVOpZynkWGmWM3keq4K/is3KlTSH5eU54UCThaFkoI5KnOqhXFiKoAoNjcAE0FNrw6ZYYGJMmu1UmUKWQpKzHWzdbEAwzyWBJvdu8AIFXxR5zRWs4Hj+W6uVjW5Gc9ebjRiwUEe5Yv7DOh0pgYIUb7iJ4DDOcnS1FQrwwSnlM1jSHDBlHlWmfzGLWJ+DoodhheDpNw5wlw6RyBosm4jTRDkX5voj00zjDIWV9NsVeA/vl3TLB5aX7PLYOi1gzb64O4cvFxu4Kb12Hpi7VrI6lkH1jvr0BpaxP5qf7O/2z8ajxovGq8bbxfUDXupeWitnMb7XyqXc5w=</latexit><latexit sha1_base64="31yzsdrJZaECvLaNQfvzLMTBcDc=">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</latexit>

if 0 < |s�1(v)| < 1<latexit sha1_base64="pmcFv/7ALXmMEy0z9o3/zPKL+fI=">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</latexit><latexit sha1_base64="pmcFv/7ALXmMEy0z9o3/zPKL+fI=">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</latexit><latexit sha1_base64="pmcFv/7ALXmMEy0z9o3/zPKL+fI=">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</latexit><latexit sha1_base64="pmcFv/7ALXmMEy0z9o3/zPKL+fI=">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</latexit>

e⇤1e1 = v2

<latexit sha1_base64="+BX3b7T03KyCL521ujZrcHV0GhQ=">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</latexit><latexit sha1_base64="+BX3b7T03KyCL521ujZrcHV0GhQ=">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</latexit><latexit sha1_base64="+BX3b7T03KyCL521ujZrcHV0GhQ=">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</latexit><latexit sha1_base64="+BX3b7T03KyCL521ujZrcHV0GhQ=">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</latexit>

e⇤1e2 = 0

<latexit sha1_base64="Zg5RQ+4pGr/E10t9qOsE5FuwLtk=">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</latexit><latexit sha1_base64="Zg5RQ+4pGr/E10t9qOsE5FuwLtk=">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</latexit><latexit sha1_base64="Zg5RQ+4pGr/E10t9qOsE5FuwLtk=">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</latexit><latexit sha1_base64="Zg5RQ+4pGr/E10t9qOsE5FuwLtk=">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</latexit>

e1e⇤1 + e2e

⇤2 = v1

<latexit sha1_base64="48Is3LyxSKDKTxteY6rB6y6Ll3A=">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</latexit><latexit sha1_base64="48Is3LyxSKDKTxteY6rB6y6Ll3A=">AAAEPnicvVJNb9NAELVrPkr4SuHIxSKKhKCKvG6cxIdIlRBSj0UltFIcovV6nKy6Xlu766aR5R/Hz+DKhRPiypG1EyBJOcCFkSw9z755M5p5YcaoVI7zydyzbt2+c3f/XuP+g4ePHjcPnryXaS4IjEjKUnERYgmMchgpqhhcZAJwEjI4Dy9fV+/nVyAkTfk7tcxgkuAZpzElWOnUtPm5CGqRsZiFk8LpOI6DEDqsAOr3HA18f+CiQQlTVO5w/UHP7fZqbh+5dZHb7x51K+6Hl+Wrv5d2/0Ha1dLDXWnP91Cl6DnIP1pLdz2vvNJTT5uturkO+yZAa9Ay1nE6Pdh7E0QpyRPgijAs5Ri5mZoUWChKGJSNIJeQYXKJZzDWkOME5KSoJyrtts5EdpwK/XFl19nNigInUi6TUDMTrOZy961K/ultnKt4MCkoz3IFnKwaxTmzVWpXl7UjKoAottQAE0H1rDaZY4GJ0vff6jKDNAEllmWjvdmAYR5JgrVJNhiBgmu1oJGaD23XczK1XZPp9RxmukasOMilfPU/BzqbqyFClG/pCeCwIGmS6G5FEOOEsmUEMc6Z0i6Q8U/cJtrFFNsMrxZJuX2GubTPQNB4V0bqJMjfMuEvmUYQpiyqttmuwH+8XUMbD+3a7CYYuR2/g946rePB2oH7xjPjufHCQEbfODZOjFNjZBDzxOTmwry2PlpfrK/WtxV1z1zXPDW2wvr+Ay2uXDs=</latexit><latexit sha1_base64="48Is3LyxSKDKTxteY6rB6y6Ll3A=">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</latexit><latexit sha1_base64="48Is3LyxSKDKTxteY6rB6y6Ll3A=">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</latexit>

LK(E) = free K-algebra on the symbols E0[E1[E1⇤<latexit sha1_base64="IUNGAzVrggc6re6k/T+qojcEH1E=">AAACq3icdZFdi9NAFIYn8WutX1UvvRlshF1Zw0y2aZsLYUEKwgqusHWrTS2T6UkbdvLBzEQoIb/Of+Cd/8ZJNhfa1QMDL++ZZ86Zc6JCJEoT8suyb92+c/fewf3eg4ePHj/pP332WeWl5DDjucjlPGIKRJLBTCdawLyQwNJIwGV09a7JX34HqZI8u9C7ApYp22RJnHCmjbXq/3A+rM4Op0dvHRxLAOycOW+Y2EAkGc4zrLeA1S 6NcqFwFbblFnITLSviEj/wKTkmrk9ocNKIIJgMfb92pt+IUzshLwtnnyGEUnrcCDoedYxHJw1D/8MEk5E3HLXMmHot7I2HJ8OGqejr2qlX/UH7tAl8U9BODFAX56v+z3Cd8zKFTHPBlFpQUuhlxaROuIC6F5YKCsav2AYWRmYsBbWs2q5q/Mo4axzn0pxM49b9k6hYqpqRmZsp01u1n2vMf+UWpY4nyyrJilJDxq8LxaXAOsfN5vA6kcC12BnBuExMr5hvmWRcm/32zBDo/pdvipnnBi795A1Op900DtAL9BIdIorG6BS9R+dohrh1ZH205tYX27Uv7K92eH3VtjrmOforbPgNmxLC8g==</latexit><latexit sha1_base64="IUNGAzVrggc6re6k/T+qojcEH1E=">AAACq3icdZFdi9NAFIYn8WutX1UvvRlshF1Zw0y2aZsLYUEKwgqusHWrTS2T6UkbdvLBzEQoIb/Of+Cd/8ZJNhfa1QMDL++ZZ86Zc6JCJEoT8suyb92+c/fewf3eg4ePHj/pP332WeWl5DDjucjlPGIKRJLBTCdawLyQwNJIwGV09a7JX34HqZI8u9C7ApYp22RJnHCmjbXq/3A+rM4Op0dvHRxLAOycOW+Y2EAkGc4zrLeA1S 6NcqFwFbblFnITLSviEj/wKTkmrk9ocNKIIJgMfb92pt+IUzshLwtnnyGEUnrcCDoedYxHJw1D/8MEk5E3HLXMmHot7I2HJ8OGqejr2qlX/UH7tAl8U9BODFAX56v+z3Cd8zKFTHPBlFpQUuhlxaROuIC6F5YKCsav2AYWRmYsBbWs2q5q/Mo4axzn0pxM49b9k6hYqpqRmZsp01u1n2vMf+UWpY4nyyrJilJDxq8LxaXAOsfN5vA6kcC12BnBuExMr5hvmWRcm/32zBDo/pdvipnnBi795A1Op900DtAL9BIdIorG6BS9R+dohrh1ZH205tYX27Uv7K92eH3VtjrmOforbPgNmxLC8g==</latexit><latexit sha1_base64="IUNGAzVrggc6re6k/T+qojcEH1E=">AAACq3icdZFdi9NAFIYn8WutX1UvvRlshF1Zw0y2aZsLYUEKwgqusHWrTS2T6UkbdvLBzEQoIb/Of+Cd/8ZJNhfa1QMDL++ZZ86Zc6JCJEoT8suyb92+c/fewf3eg4ePHj/pP332WeWl5DDjucjlPGIKRJLBTCdawLyQwNJIwGV09a7JX34HqZI8u9C7ApYp22RJnHCmjbXq/3A+rM4Op0dvHRxLAOycOW+Y2EAkGc4zrLeA1S 6NcqFwFbblFnITLSviEj/wKTkmrk9ocNKIIJgMfb92pt+IUzshLwtnnyGEUnrcCDoedYxHJw1D/8MEk5E3HLXMmHot7I2HJ8OGqejr2qlX/UH7tAl8U9BODFAX56v+z3Cd8zKFTHPBlFpQUuhlxaROuIC6F5YKCsav2AYWRmYsBbWs2q5q/Mo4axzn0pxM49b9k6hYqpqRmZsp01u1n2vMf+UWpY4nyyrJilJDxq8LxaXAOsfN5vA6kcC12BnBuExMr5hvmWRcm/32zBDo/pdvipnnBi795A1Op900DtAL9BIdIorG6BS9R+dohrh1ZH205tYX27Uv7K92eH3VtjrmOforbPgNmxLC8g==</latexit><latexit sha1_base64="IUNGAzVrggc6re6k/T+qojcEH1E=">AAACq3icdZFdi9NAFIYn8WutX1UvvRlshF1Zw0y2aZsLYUEKwgqusHWrTS2T6UkbdvLBzEQoIb/Of+Cd/8ZJNhfa1QMDL++ZZ86Zc6JCJEoT8suyb92+c/fewf3eg4ePHj/pP332WeWl5DDjucjlPGIKRJLBTCdawLyQwNJIwGV09a7JX34HqZI8u9C7ApYp22RJnHCmjbXq/3A+rM4Op0dvHRxLAOycOW+Y2EAkGc4zrLeA1S 6NcqFwFbblFnITLSviEj/wKTkmrk9ocNKIIJgMfb92pt+IUzshLwtnnyGEUnrcCDoedYxHJw1D/8MEk5E3HLXMmHot7I2HJ8OGqejr2qlX/UH7tAl8U9BODFAX56v+z3Cd8zKFTHPBlFpQUuhlxaROuIC6F5YKCsav2AYWRmYsBbWs2q5q/Mo4axzn0pxM49b9k6hYqpqRmZsp01u1n2vMf+UWpY4nyyrJilJDxq8LxaXAOsfN5vA6kcC12BnBuExMr5hvmWRcm/32zBDo/pdvipnnBi795A1Op900DtAL9BIdIorG6BS9R+dohrh1ZH205tYX27Uv7K92eH3VtjrmOforbPgNmxLC8g==</latexit>

modulo the following five types of relations:<latexit sha1_base64="f78afY4r05RA0jMP1m11UogaMg8=">AAACFXicbVDLSgMxFM34rPU16tJNsAhuLDPd+FgVRHBZwdpCW0omvdOGZpIhyVTK0K9w46+4caHiVnDn35hOZ6GtFwKHc84l95wg5kwbz/t2lpZXVtfWCxvFza3tnV13b/9ey0RRqFPJpWoGRANnAuqGGQ7NWAGJAg6NYHg11RsjUJpJcWfGMXQi0hcsZJQYS3Xd00j2Ei6xGQAOJefygYk+DtkI8NSusQyxAp659WXXLXllLx u8CPwclFA+ta771e5JmkQgDOVE65bvxaaTEmUY5TApthMNMaFD0oeWhYJEoDtpFmuCjy3Ts1cp+4TBGft7IyWR1uMosM6ImIGe16bkf1orMeF5J2UiTgwIOvsoTDg2MguNe0wBNXxsAaGK2VsxHRBFqLFNFm0J/nzkRVCvlC/K/m2lVL3O2yigQ3SETpCPzlAV3aAaqiOKHtEzekVvzpPz4rw7HzPrkpPvHKA/43z+ANr/n2M=</latexit><latexit sha1_base64="f78afY4r05RA0jMP1m11UogaMg8=">AAACFXicbVDLSgMxFM34rPU16tJNsAhuLDPd+FgVRHBZwdpCW0omvdOGZpIhyVTK0K9w46+4caHiVnDn35hOZ6GtFwKHc84l95wg5kwbz/t2lpZXVtfWCxvFza3tnV13b/9ey0RRqFPJpWoGRANnAuqGGQ7NWAGJAg6NYHg11RsjUJpJcWfGMXQi0hcsZJQYS3Xd00j2Ei6xGQAOJefygYk+DtkI8NSusQyxAp659WXXLXllLx u8CPwclFA+ta771e5JmkQgDOVE65bvxaaTEmUY5TApthMNMaFD0oeWhYJEoDtpFmuCjy3Ts1cp+4TBGft7IyWR1uMosM6ImIGe16bkf1orMeF5J2UiTgwIOvsoTDg2MguNe0wBNXxsAaGK2VsxHRBFqLFNFm0J/nzkRVCvlC/K/m2lVL3O2yigQ3SETpCPzlAV3aAaqiOKHtEzekVvzpPz4rw7HzPrkpPvHKA/43z+ANr/n2M=</latexit><latexit sha1_base64="f78afY4r05RA0jMP1m11UogaMg8=">AAACFXicbVDLSgMxFM34rPU16tJNsAhuLDPd+FgVRHBZwdpCW0omvdOGZpIhyVTK0K9w46+4caHiVnDn35hOZ6GtFwKHc84l95wg5kwbz/t2lpZXVtfWCxvFza3tnV13b/9ey0RRqFPJpWoGRANnAuqGGQ7NWAGJAg6NYHg11RsjUJpJcWfGMXQi0hcsZJQYS3Xd00j2Ei6xGQAOJefygYk+DtkI8NSusQyxAp659WXXLXllLx u8CPwclFA+ta771e5JmkQgDOVE65bvxaaTEmUY5TApthMNMaFD0oeWhYJEoDtpFmuCjy3Ts1cp+4TBGft7IyWR1uMosM6ImIGe16bkf1orMeF5J2UiTgwIOvsoTDg2MguNe0wBNXxsAaGK2VsxHRBFqLFNFm0J/nzkRVCvlC/K/m2lVL3O2yigQ3SETpCPzlAV3aAaqiOKHtEzekVvzpPz4rw7HzPrkpPvHKA/43z+ANr/n2M=</latexit><latexit sha1_base64="f78afY4r05RA0jMP1m11UogaMg8=">AAACFXicbVDLSgMxFM34rPU16tJNsAhuLDPd+FgVRHBZwdpCW0omvdOGZpIhyVTK0K9w46+4caHiVnDn35hOZ6GtFwKHc84l95wg5kwbz/t2lpZXVtfWCxvFza3tnV13b/9ey0RRqFPJpWoGRANnAuqGGQ7NWAGJAg6NYHg11RsjUJpJcWfGMXQi0hcsZJQYS3Xd00j2Ei6xGQAOJefygYk+DtkI8NSusQyxAp659WXXLXllLx u8CPwclFA+ta771e5JmkQgDOVE65bvxaaTEmUY5TApthMNMaFD0oeWhYJEoDtpFmuCjy3Ts1cp+4TBGft7IyWR1uMosM6ImIGe16bkf1orMeF5J2UiTgwIOvsoTDg2MguNe0wBNXxsAaGK2VsxHRBFqLFNFm0J/nzkRVCvlC/K/m2lVL3O2yigQ3SETpCPzlAV3aAaqiOKHtEzekVvzpPz4rw7HzPrkpPvHKA/43z+ANr/n2M=</latexit>

s(e)e = er(e) = e<latexit sha1_base64="A5AsByit0M4YpIfE/Rl7YIlXeZQ=">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</latexit><latexit sha1_base64="A5AsByit0M4YpIfE/Rl7YIlXeZQ=">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</latexit><latexit sha1_base64="A5AsByit0M4YpIfE/Rl7YIlXeZQ=">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</latexit><latexit sha1_base64="A5AsByit0M4YpIfE/Rl7YIlXeZQ=">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</latexit>

s0(e⇤)e⇤ = e⇤r0(e⇤) = e⇤<latexit sha1_base64="gvfHDtsZKIbDGXlLdTiSMYl3xmI=">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</latexit><latexit sha1_base64="sHAssrRBKeG86jKKrUmJGN3+5Hk=">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</latexit><latexit sha1_base64="sHAssrRBKeG86jKKrUmJGN3+5Hk=">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</latexit><latexit sha1_base64="cY1mlNk0VogUj+4iGXyNEgfeENY=">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</latexit>

Page 5: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

e5<latexit sha1_base64="2oTVAYPOXK7qVoTAKdaZt9kQovk=">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</latexit><latexit sha1_base64="fuQ1sFb76il7pyt7uv1eo8bJJpg=">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</latexit><latexit sha1_base64="fuQ1sFb76il7pyt7uv1eo8bJJpg=">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</latexit>

e!<latexit sha1_base64="miKXffsTgVs7S3sc7Y2C7OV8gB8=">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</latexit><latexit sha1_base64="KP/aQ8GcDmkMYALYuvJ6yN27yLs=">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</latexit><latexit sha1_base64="KP/aQ8GcDmkMYALYuvJ6yN27yLs=">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</latexit>

v!<latexit sha1_base64="+ESNGFHMjPIRmpA5ljhoZ8TRV7k=">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</latexit><latexit sha1_base64="hJARN2wzcpXVoo8WRz9Wipj7Gqc=">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</latexit><latexit sha1_base64="hJARN2wzcpXVoo8WRz9Wipj7Gqc=">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</latexit>

v1<latexit sha1_base64="8PAKmmixM9V7EuJjn4WJYmj2zAM=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">AAADXXicvVLNbtNAEN4mUEoopT8HDlxWVJEQQpEdsGgOlSp+JI5FIbRSEkXj9ThZdXdt7Y5bIquPwBWegTfgMbhy41FYxxSSCq6MZOnzNzPf7H47ca6koyD4vtZo3ri5fmvjduvO5t2te9s7u+9dVliBA5GpzJ7G4FBJgwOSpPA0twg6VngSn72s8ifnaJ3MzDua5zjWMDUylQLIU/3zSTjZ3g86QdSLwoAHnSgIe08r0OsdPIsiHnaCRewf7X599W3vy+PjyU7j9SjJRKHRkFDg3DDs5jQuwZIUCi9bo8JhDuIMpjj00IBGNy4XZ73kbc8kPM2s/wzxBbvcUYJ2bq5jX6mBZu56riL/lhsWlB6MS2nygtCIelBaKE4Zry7OE2lRkJp7AMJKf1YuZmBBkLen1V4eM8VMI9n56lUUmMQJ8B4uFxB+oAuZ0OyQd6MgpxWlYe7teZL7HlvXhF1p6v8ZyumMDsNQmhU9iwYvRKa1n1aOUtBSzRNMoVB0WY5ceoXbwj+yBK6gNlIa3gfjeB+tTK/LOE+i+yMT/5ZpjeJMJZWb7Qr8x7dr+cW72i7+bzDodnqd4K1fwBesjg32gD1kj1jInrMj9oYdswETbMo+sk/sc+NHc7252dyqSxtrv3r22Eo07/8EwHUdLg==</latexit>

v2<latexit sha1_base64="RnLauIjsfIi1c/EKrcB2wuxx9a8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">AAADXXicvVLNbtNAEN4mUEoopT8HDlxWVJEQQpEdsGgOlSp+JI5FIbRSEkXj9ThZdXdt7Y5bIquPwBWegTfgMbhy41FYxxSSCq6MZOnzNzPf7H47ca6koyD4vtZo3ri5fmvjduvO5t2te9s7u+9dVliBA5GpzJ7G4FBJgwOSpPA0twg6VngSn72s8ifnaJ3MzDua5zjWMDUylQLIU/3zSXeyvR90gqgXhQEPOlEQ9p5WoNc7eBZFPOwEi9g/2v366tvel8fHk53G61GSiUKjIaHAuWHYzWlcgiUpFF62RoXDHMQZTHHooQGNblwuznrJ255JeJpZ/xniC3a5owTt3FzHvlIDzdz1XEX+LTcsKD0Yl9LkBaER9aC0UJwyXl2cJ9KiIDX3AISV/qxczMCCIG9Pq708ZoqZRrLz1asoMIkT4D1cLiD8QBcyodkh70ZBTitKw9zb8yT3PbauCbvS1P8zlNMZHYahNCt6Fg1eiExrP60cpaClmieYQqHoshy59Aq3hX9kCVxBbaQ0vA/G8T5amV6XcZ5E90cm/i3TGsWZSio32xX4j2/X8ot3tV3832DQ7fQ6wVu/gC9YHRvsAXvIHrGQPWdH7A07ZgMm2JR9ZJ/Y58aP5npzs7lVlzbWfvXssZVo3v8Jw2wdLw==</latexit>

v3<latexit sha1_base64="aCJXJ5RlxA9vJSXn+kHy1M4mML0=">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</latexit><latexit sha1_base64="7+An/e4ZjGTsSKaG/UAenbk8Nsc=">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</latexit><latexit sha1_base64="7+An/e4ZjGTsSKaG/UAenbk8Nsc=">AAADXXicvVLNbtNAEN4mUIop/T1w4LKiioQQiuwUi+ZQqeJH4lgUQivFUbRej51Vd9fW7rglsvIIXOEZeAMegys3HoV1TCGp4MpIlj5/M/PN7rcTF1JY9P3va632rdvrdzbuevc2729t7+zuvbd5aTgMeS5zcx4zC1JoGKJACeeFAaZiCWfxxcs6f3YJxopcv8NZAWPFMi1SwRk6anA5OZzsHPhdP+yHgU/9bugH/cMa9PtHz8KQBl1/EQcne19ffdv/8uR0stt6HSU5LxVo5JJZOwp6BY4rZlBwCXMvKi0UjF+wDEYOaqbAjqvFWee045iEprlxn0a6YJc7KqasnanYVSqGU3szV5N/y41KTI/GldBFiaB5MygtJcWc1heniTDAUc4cYNwId1bKp8wwjs4er7M8JoNcAZrZ6lUk04nlzHm4XIDwAa9EgtNj2gv9AleURoWz52nhekxTE/SEbv6nILIpHgeB0Ct6BjRc8VwpN62KUqaEnCWQslLivIpseo073D2yYFSyxkih6YBpSwdgRHpTxjoS7B+Z+LeMF8W5TGo3OzX4j2/nucW73i76bzDsdftd/61bwBekiQ3ykDwij0lAnpMT8oackiHhJCMfySfyufWjvd7ebG81pa21Xz37ZCXaD34CxmMdMA==</latexit>

v4<latexit sha1_base64="5o7IKDY9gLFdRStvBpyGFyzmiOI=">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</latexit><latexit sha1_base64="DY7vSTAraABkoaKhE1CBCXv4ZaE=">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</latexit><latexit sha1_base64="DY7vSTAraABkoaKhE1CBCXv4ZaE=">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</latexit>

v5<latexit sha1_base64="XEnGBwIhIUAc946elKahyxHOr10=">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</latexit><latexit sha1_base64="yaUbGn+TXLSwb/L1QU3Kk9yCgMc=">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</latexit><latexit sha1_base64="yaUbGn+TXLSwb/L1QU3Kk9yCgMc=">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</latexit>

v6<latexit sha1_base64="UfomTyGXDzzJ10RXwIfU4GSYSXE=">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</latexit><latexit sha1_base64="3gg7qt9+5vGUIG1FQwwKinA/wxc=">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</latexit><latexit sha1_base64="3gg7qt9+5vGUIG1FQwwKinA/wxc=">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</latexit>

e2<latexit sha1_base64="+qvft35mNCYBd7mHkko9V+wUF/c=">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</latexit><latexit sha1_base64="4TWgrdRvjtxoRH9cYpisFS/0ZOc=">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</latexit><latexit sha1_base64="4TWgrdRvjtxoRH9cYpisFS/0ZOc=">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</latexit>

e1<latexit sha1_base64="Gahtq2xaFc9C2zq3tCEmh3z/KjE=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">AAADXXicvVLBbhMxEHUTKCGU0sKBAxeLKhIHFK0jlSaHSpUQEhKXohBaKYmiWe9sYtX2ruxZSrTKJ3CF/+BbeuHGT3DH26XQVHBlpJXevpl5Yz9PnGvlKYq+bTSat25v3mndbd/bur/9YGf34XufFU7iSGY6c6cxeNTK4ogUaTzNHYKJNZ7EZy+r/MkHdF5l9h0tc5wamFuVKgkUqCHOxGxnL+pGUSSE4BUQBy+iAAaDfk/0uahSIfaOWj++Xlw03hzPdhuvJkkmC4OWpAbvx6KX07QER0pqXLUnhccc5BnMcRygBYN+Wl6edcU7gUl4mrnwWeKX7PWOEoz3SxOHSgO08DdzFfm33LigtD8tlc0LQivrQWmhOWW8ujhPlENJehkASKfCWblcgANJwZ525/qYOWYGyS3Xr6LBJl5C8PB6AeFHOlcJLQ55bz/KaU1pnAd7nuehx9U1oqds/b9ANV/QoRDKruk5tHguM2PCtHKSglF6mWAKhaZVOfHpFe7I8MgKuIbaSGX5EKznQ3QqvSnjA4n+j0z8W6Y9iTOdVG52KvAf364dFu9qu/i/wajXHXSjt2EB+6yOFnvCnrJnTLADdsRes2M2YpLN2Sf2mX1pfG9uNrea23VpY+NXzyO2Fs3HPwG3fR3b</latexit>

e3<latexit sha1_base64="u6aps99kjMZnFt6LACGZVHxr8GA=">AAADXXicvVLBbhMxEHUTKCGU0sKBAxeLKhIHFK2DoMmhUiWExLEohFZKomjWO5tYtb0re5YSrfIJXOE/+AJ+gxs/wR1vl0JSwZWRVnr7ZuaN/TxxrpWnKPq21WjeuLl9q3W7fWfn7u69vf3773xWOIkjmenMncXgUSuLI1Kk8Sx3CCbWeBqfv6zyp+/ReZXZt7TMcWpgblWqJFCghjh7Nts7iLpRFAkheAXE4YsogMGg3xN9LqpUiIPj1o8vXxljJ7P9xqtJksnCoCWpwfux6OU0LcGRkhpX7UnhMQd5DnMcB2jBoJ+Wl2dd8U5gEp5mLnyW+CW73lGC8X5p4lBpgBb+eq4i/5YbF5T2p6WyeUFoZT0oLTSnjFcX54lyKEkvAwDpVDgrlwtwICnY0+6sj5ljZpDccvMqGmziJQQP1wsIP9CFSmhxxHvPo5w2lMZ5sOdpHnpcXSN6ytb/C1TzBR0JoeyGnkOLFzIzJkwrJykYpZcJplBoWpUTn17hjgyPrIBrqI1Ulg/Bej5Ep9LrMj6Q6P/IxL9l2pM400nlZqcC//Ht2mHxrraL/xuMet1BN3oTFrDP6mixR+wxe8IEO2TH7DU7YSMm2Zx9ZJ/Y58b35nZzp7lblza2fvU8YBvRfPgTX/AcqA==</latexit><latexit sha1_base64="ko+763tzlQVosGPwibi3OupeYmY=">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</latexit><latexit sha1_base64="ko+763tzlQVosGPwibi3OupeYmY=">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</latexit>

e4<latexit sha1_base64="u2R2RalfWEo8fhoEzg7jafnylrE=">AAADXXicvVLBbhMxEHUTKCGU0sKBAxeLKhIHFK0joMmhUiWExLEohFZKomjWO5tYtb0re5YSrfIJXOE/+AJ+gxs/wR1vl0JSwZWRVnr7ZuaN/TxxrpWnKPq21WjeuLl9q3W7fWfn7u69vf3773xWOIkjmenMncXgUSuLI1Kk8Sx3CCbWeBqfv6zyp+/ReZXZt7TMcWpgblWqJFCghjh7Nts7iLpRFAkheAXE4YsogMGg3xN9LqpUiIPj1o8vXxljJ7P9xqtJksnCoCWpwfux6OU0LcGRkhpX7UnhMQd5DnMcB2jBoJ+Wl2dd8U5gEp5mLnyW+CW73lGC8X5p4lBpgBb+eq4i/5YbF5T2p6WyeUFoZT0oLTSnjFcX54lyKEkvAwDpVDgrlwtwICnY0+6sj5ljZpDccvMqGmziJQQP1wsIP9CFSmhxxHvPo5w2lMZ5sOdpHnpcXSN6ytb/C1TzBR0JoeyGnkOLFzIzJkwrJykYpZcJplBoWpUTn17hjgyPrIBrqI1Ulg/Bej5Ep9LrMj6Q6P/IxL9l2pM400nlZqcC//Ht2mHxrraL/xuMet1BN3oTFrDP6mixR+wxe8IEO2TH7DU7YSMm2Zx9ZJ/Y58b35nZzp7lblza2fvU8YBvRfPgTYuccqQ==</latexit><latexit sha1_base64="qjGof5nbXTi2LG7wMGqXhXEqGtw=">AAADXXicvVLBbhMxEHUTKCGU0sKBAxeLKhIHFK0joMmhUiWEhMSlKIRWSqJo1jubWLW9K3uWEq36CVzhP/iWXrjxE9zxdikkFVwZaaW3b2be2M8T51p5iqJvG43mjZubt1q323e27m7f29m9/95nhZM4kpnO3EkMHrWyOCJFGk9yh2Bijcfx6csqf/wBnVeZfUfLHKcG5lalSgIFaoizZ7OdvagbRZEQgldA7L+IAhgM+j3R56JKhdg7bP34enHReHM02228miSZLAxakhq8H4teTtMSHCmp8bw9KTzmIE9hjuMALRj00/LyrOe8E5iEp5kLnyV+ya52lGC8X5o4VBqghb+eq8i/5cYFpf1pqWxeEFpZD0oLzSnj1cV5ohxK0ssAQDoVzsrlAhxICva0O6tj5pgZJLdcv4oGm3gJwcPVAsKPdKYSWhzw3vMopzWlcR7seZqHHlfXiJ6y9f8C1XxBB0Iou6bn0OKZzIwJ08pJCkbpZYIpFJrOy4lPr3BHhkdWwDXURirLh2A9H6JT6XUZH0j0f2Ti3zLtSZzppHKzU4H/+HbtsHhX28X/DUa97qAbvQ0L2Gd1tNgj9pg9YYLts0P2mh2xEZNszj6xz+xL43tzs7nV3K5LGxu/eh6wtWg+/AnAYh3e</latexit><latexit sha1_base64="qjGof5nbXTi2LG7wMGqXhXEqGtw=">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</latexit>

e6<latexit sha1_base64="4hpldoBTI3TdciTk2lw/afLqBL4=">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</latexit><latexit sha1_base64="XK6KnUlmY1y/hiZoiu7q7bTAgSU=">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</latexit><latexit sha1_base64="XK6KnUlmY1y/hiZoiu7q7bTAgSU=">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</latexit>

e7<latexit sha1_base64="ZikDrdAbsc1p8mE1uoX8u32g7fg=">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</latexit><latexit sha1_base64="DItlr6l1+XJLuVwmgc5P4ZU9qUE=">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</latexit><latexit sha1_base64="DItlr6l1+XJLuVwmgc5P4ZU9qUE=">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</latexit>e8

<latexit sha1_base64="lycQNS7HDk/TwRHKTdDQ/1kZ1bI=">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</latexit><latexit sha1_base64="I4p7JkHKI5C2HUX4sU7SwGQkrL4=">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</latexit><latexit sha1_base64="I4p7JkHKI5C2HUX4sU7SwGQkrL4=">AAADXXicvVLBbhMxEHUTKCGU0sKBAxeLKhIHFK0jlSaHSpUQEhKXohBaKYmiWe9sYtX2ruxZSrTKJ3CF/+BbeuHGT3DH26XQVHBlpJXevpl5Yz9PnGvlKYq+bTSat25v3mndbd/bur/9YGf34XufFU7iSGY6c6cxeNTK4ogUaTzNHYKJNZ7EZy+r/MkHdF5l9h0tc5wamFuVKgkUqCHO+rOdvagbRZEQgldAHLyIAhgM+j3R56JKhdg7av34enHReHM82228miSZLAxakhq8H4teTtMSHCmpcdWeFB5zkGcwx3GAFgz6aXl51hXvBCbhaebCZ4lfstc7SjDeL00cKg3Qwt/MVeTfcuOC0v60VDYvCK2sB6WF5pTx6uI8UQ4l6WUAIJ0KZ+VyAQ4kBXvanetj5pgZJLdcv4oGm3gJwcPrBYQf6VwltDjkvf0opzWlcR7seZ6HHlfXiJ6y9f8C1XxBh0Iou6bn0OK5zIwJ08pJCkbpZYIpFJpW5cSnV7gjwyMr4BpqI5XlQ7CeD9Gp9KaMDyT6PzLxb5n2JM50UrnZqcB/fLt2WLyr7eL/BqNed9CN3oYF7LM6WuwJe8qeMcEO2BF7zY7ZiEk2Z5/YZ/al8b252dxqbteljY1fPY/YWjQf/wTMPh3i</latexit>

e⇤1

<latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">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</latexit><latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">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</latexit><latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">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</latexit><latexit sha1_base64="03/N6Q588eDtdmBP28plLRNq9BE=">AAADX3icvVJdb9MwFPVaPkqArYMnxItFVQkhVCWhrN3DpEkIicehUTapKZXj3LTWbCeybxhR1N/AK/w0XvklOEsH7QSvXMnS8bmfPr5xLoVF3/+x02rfun3nbueed//Bw9297v6jjzYrDIcJz2RmzmNmQQoNExQo4Tw3wFQs4Sy+eFP7zz6DsSLTH7DMYabYQotUcIaOmsA8+PRi3u35g8PxQTg8oP7A90dBGNQgHA1fDWngmNp6ZG0n8/3W2yjJeKFAI5fM2mkQ5jirmEHBJay8qLCQM37BFjB1UDMFdlZdTbuifcckNM2MOxrpFbuZUTFlbaliF6kYLu1NX03+zTctMB3PKqHzAkHzplFaSIoZrZ9OE2GAoywdYNwINyvlS2YYRyfQVpcFZArQlCuvv9lAMp1YzpyKGxERwhe8FAkuj2j42s9xOyd38rzMXY5pYoJQ6Oa+BLFY4lEQCL1Vz4CGS54p5bpVUcqUkGUCKSskrqrIpte4z903C0Yla4QUmp4ybekpGJHeLGMdCfZPmfh3GS+KM5nUavZr8B//znOLd71d9N9gEg4OB8F7v3c8Xm9ghzwlz8hzEpAROSbvyAmZEE4E+Uq+ke+tn+1Oe7fdbUJbO+ucx2TL2k9+AePrGqA=</latexit>

e⇤2

<latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit><latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit><latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit><latexit sha1_base64="nxs+BTNbOgtfo8YTvlc982HdkMI=">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</latexit>

e⇤3

<latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">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</latexit><latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">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</latexit><latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">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</latexit><latexit sha1_base64="xd0emvDgh8+yTbjJVVn0ADOGvCw=">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</latexit>

e⇤4

<latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">AAADX3icvVJdb9MwFPVaPkqArYMnxItFVQkhVCWhrN3DpEkIicehUTapKZXj3LTWbCeybxhR1N/AK/w0XvklOEsH7QSvXMnS8bmfPr5xLoVF3/+x02rfun3nbueed//Bw9297v6jjzYrDIcJz2RmzmNmQQoNExQo4Tw3wFQs4Sy+eFP7zz6DsSLTH7DMYabYQotUcIaOmsB8+OnFvNvzB4fjg3B4QP2B74+CMKhBOBq+GtLAMbX1yNpO5vutt1GS8UKBRi6ZtdMgzHFWMYOCS1h5UWEhZ/yCLWDqoGYK7Ky6mnZF+45JaJoZdzTSK3Yzo2LK2lLFLlIxXNqbvpr8m29aYDqeVULnBYLmTaO0kBQzWj+dJsIAR1k6wLgRblbKl8wwjk6grS4LyBSgKVdef7OBZDqxnDkVNyIihC94KRJcHtHwtZ/jdk7u5HmZuxzTxASh0M19CWKxxKMgEHqrngENlzxTynWropQpIcsEUlZIXFWRTa9xn7tvFoxK1ggpND1l2tJTMCK9WcY6EuyfMvHvMl4UZzKp1ezX4D/+necW73q76L/BJBwcDoL3fu94vN7ADnlKnpHnJCAjckzekRMyIZwI8pV8I99bP9ud9m6724S2dtY5j8mWtZ/8AuzWGqM=</latexit><latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">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</latexit><latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">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</latexit><latexit sha1_base64="FhcDO4SpZ0ARlPk+d79iVfOW+bI=">AAADX3icvVJdb9MwFPVaPkqArYMnxItFVQkhVCWhrN3DpEkIicehUTapKZXj3LTWbCeybxhR1N/AK/w0XvklOEsH7QSvXMnS8bmfPr5xLoVF3/+x02rfun3nbueed//Bw9297v6jjzYrDIcJz2RmzmNmQQoNExQo4Tw3wFQs4Sy+eFP7zz6DsSLTH7DMYabYQotUcIaOmsB8+OnFvNvzB4fjg3B4QP2B74+CMKhBOBq+GtLAMbX1yNpO5vutt1GS8UKBRi6ZtdMgzHFWMYOCS1h5UWEhZ/yCLWDqoGYK7Ky6mnZF+45JaJoZdzTSK3Yzo2LK2lLFLlIxXNqbvpr8m29aYDqeVULnBYLmTaO0kBQzWj+dJsIAR1k6wLgRblbKl8wwjk6grS4LyBSgKVdef7OBZDqxnDkVNyIihC94KRJcHtHwtZ/jdk7u5HmZuxzTxASh0M19CWKxxKMgEHqrngENlzxTynWropQpIcsEUlZIXFWRTa9xn7tvFoxK1ggpND1l2tJTMCK9WcY6EuyfMvHvMl4UZzKp1ezX4D/+necW73q76L/BJBwcDoL3fu94vN7ADnlKnpHnJCAjckzekRMyIZwI8pV8I99bP9ud9m6724S2dtY5j8mWtZ/8AuzWGqM=</latexit>

e⇤5

<latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit><latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit><latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit><latexit sha1_base64="2vK31ii53HSbfiLYjYzzk8si8lE=">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</latexit>

e⇤6

<latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit><latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit><latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit><latexit sha1_base64="Ip0ud41mMmx2f8+3iOo35R3RZ6s=">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</latexit>

e⇤7

<latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">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</latexit><latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">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</latexit><latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">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</latexit><latexit sha1_base64="YtL6pAR/fLFPm8B6/SzfwTRD52I=">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</latexit>

e⇤8

<latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">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</latexit><latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">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</latexit><latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">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</latexit><latexit sha1_base64="27TtswGVLTElJwj0RgyEed4D3Jc=">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</latexit>

e⇤!

<latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">AAADZHicvVLdahNBFJ4m/tRotbV4JchgCIhI2F1jk14UCiJ4WamxxWwsZ2fPJkNnZpeZs9aw5C281ffyCXwNZ5tUk6K3Hhj45ju/881JCiUdBcGPjUbzxs1btzfvtO7e27r/YHvn4QeXl1bgUOQqt6cJOFTS4JAkKTwtLIJOFJ4k569r/8lntE7m5j3NChxrmBiZSQHkqY94FucaJ/Dp+dl2O+juD/ai3h4PukHQD6OwBlG/97LHQ8/U1mZLOzrbabyJ01yUGg0JBc6NwqigcQWWpFA4b8WlwwLEOUxw5KEBjW5cXY485x3PpDzLrT+G+CW7mlGBdm6mEx+pgabuuq8m/+YblZQNxpU0RUloxKJRVipOOa/fz1NpUZCaeQDCSj8rF1OwIMirtNZlgl4asrN5q7PaQIFJnQAv5UpETPiFLmRK0wMevQoKWs8pvDwvCp9jFzFhJM3iPkU5mdJBGEqzVs+iwQuRa+27VXEGWqpZihmUiuZV7LIr3BH+ryVwBQshpeHHYBw/Riuz62WcJ9H9KZP8LtOKk1yltZqdGvzHv2v5xbvaLv5vMIy6+93wXdA+HCw3cJM9Zk/ZMxayPjtkb9kRGzLBDPvKvrHvjZ/NreZu89EitLGxzNlla9Z88gs6uh0G</latexit><latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">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</latexit><latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">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</latexit><latexit sha1_base64="MPgPbkXGQzKiOQvZasVjTXvg+Kw=">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</latexit>

= v1

�e1 � v2

�e⇤3e

⇤4(e3 + e4)

<latexit sha1_base64="ctdUD+30hXiGnwa31pLgB8I/KUo=">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</latexit><latexit sha1_base64="Os2xb//6Q1Bd53IUYU4f5VstZ3k=">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</latexit><latexit sha1_base64="Os2xb//6Q1Bd53IUYU4f5VstZ3k=">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</latexit><latexit sha1_base64="ope2Vgmvj0RaGKU5XVUMQfSXekY=">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</latexit>

= e1e⇤3e

⇤4(e3 + e4)

<latexit sha1_base64="Pzd32tDwU8gQLPUm2pZ8XaVEHhg=">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</latexit><latexit sha1_base64="JgorJD8rqnzuREsa3VFlqt01dWs=">AAADc3icvVJNbxMxEHUTPkr4SuHAAVRZLZFKC1E2gIBDpAqExLFVCa2UpKtZ72xi1fau7FlKtMqRX8IV7v0r/AbunHGyBZKUMyOt9Pxm5s36eaJMSUet1veVSvXS5StXV6/Vrt+4eet2fe3OB5fmVmBXpCq1RxE4VNJglyQpPMosgo4UHkYnb6b5w49onUzNexpnONAwNDKRAshTYf1eB8MAw6fH2xg+O97e8nDHo0dhfbPVbM2CXwTBOdjcXT/b//F5/WwvXKu87cepyDUaEgqc6wXtjAYFWJJC4aTWzx1mIE5giD0PDWh0g2J2gwlveCbmSWr9Z4jP2PmOArRzYx35Sg00csu5KfmvXC+n5OWgkCbLCY0oByW54pTyqR08lhYFqbEHIKz0/8rFCCwI8qbVGvNjhphqJDtevIoCEzsB3tn5AsJPdCpjGnV4+3krowWlXubteZz5HlvWBG1pyvMI5XBEnSCQZkHPosFTkWrtpxX9BLRU4xgTyBVNir5LfuOG8E8vgSsojZSGH4Bx/ACtTJZlnCfR/ZWJ/sjU+lGq4qmbjSn4j29X84sXLK/ZRdBtN181g32/gK9ZGavsPttgWyxgL9gue8f2WJcJNmFf2Ff2rfKz+qC6UX1YllZWznvusoWoPvkFOIYkGQ==</latexit><latexit sha1_base64="JgorJD8rqnzuREsa3VFlqt01dWs=">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</latexit><latexit sha1_base64="Wk0yYQ3RCM57p4bHOQNtAEpxwnU=">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</latexit>

= e1e⇤3

<latexit sha1_base64="FphTPJq0ECi/axeRfYGqTUPAcIM=">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</latexit><latexit sha1_base64="KLM0kN45y7LFFWO2L9FqeRSJzus=">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</latexit><latexit sha1_base64="KLM0kN45y7LFFWO2L9FqeRSJzus=">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</latexit><latexit sha1_base64="g5YIg+qZ8WltN9yacUlsxTmhnLU=">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</latexit>

= e1e⇤3v2

<latexit sha1_base64="zeSUswO5R0ZQ0SH3M4l7Qqzxjpo=">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</latexit><latexit sha1_base64="zeSUswO5R0ZQ0SH3M4l7Qqzxjpo=">AAADZnicvVLbbtNAEN0mXEq4tAUhHnhZEUVCCEW2AQEPkSoQEo9FJbRSHKLxepysuru2dsctlpXf4BV+i0/gL9jEAZKUZ0aydPbMzJn12UkKJR0FwY+dVvvK1WvXd290bt66fWdv/+DuJ5eXVuBQ5Cq3pwk4VNLgkCQpPC0sgk4UniRnbxf5k3O0TubmI1UFjjVMjcykAPJUPMBJiJNnn5+cT6LJfjfoB8vgl0G4Al22iqPJQetdnOai1GhIKHBuFEYFjWuwJIXCeScuHRYgzmCKIw8NaHTjennpOe95JuVZbv1niC/Z9Y4atHOVTnylBpq57dyC/FduVFL2alxLU5SERjSDslJxyvnCAZ5Ki4JU5QEIK/1duZiBBUHep05vfcwUc41kq81fUWBSJ8CbuV5A+IUuZEqzAY9eBAVtKI0Kb8/TwvfYpiaMpGnOM5TTGQ3CUJoNPYsGL0SutZ9WxxloqaoUMygVzevYZb9xT/jXlsAVNEZKw4/BOH6MVmbbMs6T6P7KJH9kOnGSq3ThZm8B/uPbdfzihdtrdhkMo/7rfvjheffwzWoDd9lD9og9ZiF7yQ7Ze3bEhkywgn1l39j31s/2Xvt++0FT2tpZ9dxjG9HmvwDeGBzt</latexit><latexit sha1_base64="zeSUswO5R0ZQ0SH3M4l7Qqzxjpo=">AAADZnicvVLbbtNAEN0mXEq4tAUhHnhZEUVCCEW2AQEPkSoQEo9FJbRSHKLxepysuru2dsctlpXf4BV+i0/gL9jEAZKUZ0aydPbMzJn12UkKJR0FwY+dVvvK1WvXd290bt66fWdv/+DuJ5eXVuBQ5Cq3pwk4VNLgkCQpPC0sgk4UniRnbxf5k3O0TubmI1UFjjVMjcykAPJUPMBJiJNnn5+cT6LJfjfoB8vgl0G4Al22iqPJQetdnOai1GhIKHBuFEYFjWuwJIXCeScuHRYgzmCKIw8NaHTjennpOe95JuVZbv1niC/Z9Y4atHOVTnylBpq57dyC/FduVFL2alxLU5SERjSDslJxyvnCAZ5Ki4JU5QEIK/1duZiBBUHep05vfcwUc41kq81fUWBSJ8CbuV5A+IUuZEqzAY9eBAVtKI0Kb8/TwvfYpiaMpGnOM5TTGQ3CUJoNPYsGL0SutZ9WxxloqaoUMygVzevYZb9xT/jXlsAVNEZKw4/BOH6MVmbbMs6T6P7KJH9kOnGSq3ThZm8B/uPbdfzihdtrdhkMo/7rfvjheffwzWoDd9lD9og9ZiF7yQ7Ze3bEhkywgn1l39j31s/2Xvt++0FT2tpZ9dxjG9HmvwDeGBzt</latexit><latexit sha1_base64="zeSUswO5R0ZQ0SH3M4l7Qqzxjpo=">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</latexit>

v1v2 = 0<latexit sha1_base64="k3KrVAVbgYL7vwfNEZfxHXPbSUU=">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</latexit><latexit sha1_base64="1hR2IQ6wu2ic2hPxZJb8K/Q2knI=">AAADjXicvVLNbhMxEHaz/JTwl5YjUmVRReJQReuUpY1EUAVCcGxVQitlo8jrnU2s2t6V7U2JVnvkGXiVXrjCM/AMvATeLIGkgisjWfo888031ueJMsGN9f3vGw3vxs1btzfvNO/eu//gYWtr+4NJc81gwFKR6vOIGhBcwcByK+A800BlJOAsunhd1c9moA1P1Xs7z2Ak6UTxhDNqXWrcIkW4EBnqSTQq/I4f9ALi7/mdwCe9/Qr0eofPgqCcjcls3C37/ri1u6ThJQ0vaZh0/EXsHu1cnfz4tHN1PN5qvAnjlOUSlGWCGjMk3cyOCqotZwLKZpgbyCi7oBMYOqioBDMqFs8qcdtlYpyk2h1l8SK72lFQacxcRo4pqZ2a67Uq+bfaMLfJ4ajgKsstKFYPSnKBbYoro3DMNTAr5g5Qprl7K2ZTqimzzs61KRNIJVg9L5vt1QGCqtgw6jxfYYQWPtpLHttpH3cDP7PrPZmzZy9zPbrmkC5X9X0KfDK1fUK4WtPToOCSpVK6aUWYUMnFPIaE5sKWRWiSJW4ztxScYkFrI7nCp1QZfAqaJ9dljEuC+SMT/ZZphlEq4srNdgX+49813eIttwv/Gwy6nV6HnLgFfIXq2ESP0RP0FBF0gI7QO3SMBoihz+gL+oq+eS3vuffCe1lTGxu/eh6htfDe/gTVYyvI</latexit><latexit sha1_base64="1hR2IQ6wu2ic2hPxZJb8K/Q2knI=">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</latexit><latexit sha1_base64="YcqSIeN6UX+LyTwH1QNSUoWtO6A=">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</latexit>

e⇤4e3 = 0

<latexit sha1_base64="v9BPKm7/kqxx7iDO79LtQzERBDA=">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</latexit><latexit sha1_base64="R9/rOVR4K9yoMcc3g7ff+nS/eoc=">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</latexit><latexit sha1_base64="R9/rOVR4K9yoMcc3g7ff+nS/eoc=">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</latexit><latexit sha1_base64="v9yQx+D0Y8tuCERIKqAoi4ctfEI=">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</latexit>

e⇤4e4 = v2

<latexit sha1_base64="bOjZLxpq9qNSgbVgTiU5ibY4j38=">AAAD43icvVJNb9NAEN3EfJTw0ZQeAckiioRQFe26+fIhUgVC4lhUQislIVqvx8mq67W1u26JLJ+5cEJc+WH8CP4D6yRAknJmJEvPb968Wc1MkAquDcY/KlXn1u07d/fu1e4/ePhov37w+INOMsVgyBKRqIuAahBcwtBwI+AiVUDjQMB5cPm6zJ9fgdI8ke/NIoVJTGeSR5xRY6lp/XM+XpqM1CyY5Ljl97teu3uEWxj3iEdK4PXax+0Cpu2PL4sdNcaYkKUIk14XW+D7fY/0S3Ux2BV3/A4pNR1M/OO1uN3pFFdTr5jWG0s7G+5NQNaggdZxOj2ovhmHCctikIYJqvWIeKmZ5FQZzgQUtXGmIaXsks5gZKGkMehJvnxR4TYtE7pRouwnjbtkNytyGmu9iAOrjKmZ691cSf4rN8pM1J/kXKaZAclWjaJMuCZxy/G7IVfAjFhYQJni9q0um1NFmbFL2uoygyQGoxZFrbnZQFAZakbtJjcUYwOfzDUPzXzgeh2cmu2a1I7nKLU1aqUhHper/znw2dwMCOFyy0+BhGuWxLHtlo8jGnOxCCGimTD2BnT0GzeZPTVOXUFXg+TSPaNSu2egeLRroy0J+q9N8MemNg4SEZbTbJbgP+6uZg+P7J7ZTTD0Wn6LvGs3Tl6tL3APPUHP0QtEUA+doLfoFA0RQz8rh5WnlWdO5HxxvjrfVtJqZV1ziLbC+f4Lp+1ASg==</latexit><latexit sha1_base64="bOjZLxpq9qNSgbVgTiU5ibY4j38=">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</latexit><latexit sha1_base64="bOjZLxpq9qNSgbVgTiU5ibY4j38=">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</latexit><latexit sha1_base64="bOjZLxpq9qNSgbVgTiU5ibY4j38=">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</latexit>

e⇤3v2 = e⇤

3<latexit sha1_base64="ddjGnjHqs/kcl+2HXXP+cbwaZP4=">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</latexit><latexit sha1_base64="ddjGnjHqs/kcl+2HXXP+cbwaZP4=">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</latexit><latexit sha1_base64="ddjGnjHqs/kcl+2HXXP+cbwaZP4=">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</latexit><latexit sha1_base64="ddjGnjHqs/kcl+2HXXP+cbwaZP4=">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</latexit>

v1e1 = e1<latexit sha1_base64="LkNcw25JXkVu6+IE2GtAUKbm93A=">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</latexit><latexit sha1_base64="LkNcw25JXkVu6+IE2GtAUKbm93A=">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</latexit><latexit sha1_base64="LkNcw25JXkVu6+IE2GtAUKbm93A=">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</latexit><latexit sha1_base64="LkNcw25JXkVu6+IE2GtAUKbm93A=">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</latexit>

(e1e⇤1 + e2e

⇤2)(e1 � v2)e

⇤3e

⇤4(e3 + e4) =

<latexit sha1_base64="4xsKQwAO9l2UKlLP5AoDKuCDaiI=">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</latexit><latexit sha1_base64="4xsKQwAO9l2UKlLP5AoDKuCDaiI=">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</latexit><latexit sha1_base64="4xsKQwAO9l2UKlLP5AoDKuCDaiI=">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</latexit><latexit sha1_base64="4xsKQwAO9l2UKlLP5AoDKuCDaiI=">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</latexit>

v1 = e1e⇤1 + e2e

⇤2

<latexit sha1_base64="uOgAOED4xHnfbIsTzB7yPzGQZZU=">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</latexit><latexit sha1_base64="uOgAOED4xHnfbIsTzB7yPzGQZZU=">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</latexit><latexit sha1_base64="uOgAOED4xHnfbIsTzB7yPzGQZZU=">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</latexit><latexit sha1_base64="uOgAOED4xHnfbIsTzB7yPzGQZZU=">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</latexit>

Page 6: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Mn(K)<latexit sha1_base64="YZhnAIybw35uFRHvDK/QMaXJz2k=">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</latexit><latexit sha1_base64="YZhnAIybw35uFRHvDK/QMaXJz2k=">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</latexit><latexit sha1_base64="YZhnAIybw35uFRHvDK/QMaXJz2k=">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</latexit><latexit sha1_base64="YZhnAIybw35uFRHvDK/QMaXJz2k=">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</latexit>

LK(An) =<latexit sha1_base64="9pUrTfJPb5eeLEzbn6u34YMEEsM=">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</latexit><latexit sha1_base64="9pUrTfJPb5eeLEzbn6u34YMEEsM=">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</latexit><latexit sha1_base64="9pUrTfJPb5eeLEzbn6u34YMEEsM=">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</latexit><latexit sha1_base64="9pUrTfJPb5eeLEzbn6u34YMEEsM=">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</latexit>v1

<latexit sha1_base64="8PAKmmixM9V7EuJjn4WJYmj2zAM=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">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</latexit>

...<latexit sha1_base64="k5fPkdaDn8Mbouceg63xrCwZPqA=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0i8qLeiF48VjS20oWy2m3bpZhN2J0IJ/QlePKh49R9589+4bXPQ6oOBx3szzMyLMikMet6XU1lZXVvfqG7WtrZ3dvfq+wcPJs014wFLZao7ETVcCsUDFCh5J9OcJpHk7Wh8PfPbj1wbkap7nGQ8TOhQiVgwila6c123X294rjcH+Uv8kjSgRKtf/+wNUpYnXCGT1Jiu72UYFlSjYJJPa73c8IyyMR3yrqWKJtyExfzUKTmxyoDEqbalkMzVnxMFTYyZJJHtTCiOzLI3E//zujnGF2EhVJYjV2yxKM4lwZTM/iYDoTlDObGEMi3srYSNqKYMbTo1G4K//PJfEpy5l65/6zWaV2UaVTiCYzgFH86hCTfQggAYDOEJXuDVkc6z8+a8L1orTjlzCL/gfHwDuOeM8g==</latexit><latexit sha1_base64="k5fPkdaDn8Mbouceg63xrCwZPqA=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0i8qLeiF48VjS20oWy2m3bpZhN2J0IJ/QlePKh49R9589+4bXPQ6oOBx3szzMyLMikMet6XU1lZXVvfqG7WtrZ3dvfq+wcPJs014wFLZao7ETVcCsUDFCh5J9OcJpHk7Wh8PfPbj1wbkap7nGQ8TOhQiVgwila6c123X294rjcH+Uv8kjSgRKtf/+wNUpYnXCGT1Jiu72UYFlSjYJJPa73c8IyyMR3yrqWKJtyExfzUKTmxyoDEqbalkMzVnxMFTYyZJJHtTCiOzLI3E//zujnGF2EhVJYjV2yxKM4lwZTM/iYDoTlDObGEMi3srYSNqKYMbTo1G4K//PJfEpy5l65/6zWaV2UaVTiCYzgFH86hCTfQggAYDOEJXuDVkc6z8+a8L1orTjlzCL/gfHwDuOeM8g==</latexit><latexit sha1_base64="k5fPkdaDn8Mbouceg63xrCwZPqA=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0i8qLeiF48VjS20oWy2m3bpZhN2J0IJ/QlePKh49R9589+4bXPQ6oOBx3szzMyLMikMet6XU1lZXVvfqG7WtrZ3dvfq+wcPJs014wFLZao7ETVcCsUDFCh5J9OcJpHk7Wh8PfPbj1wbkap7nGQ8TOhQiVgwila6c123X294rjcH+Uv8kjSgRKtf/+wNUpYnXCGT1Jiu72UYFlSjYJJPa73c8IyyMR3yrqWKJtyExfzUKTmxyoDEqbalkMzVnxMFTYyZJJHtTCiOzLI3E//zujnGF2EhVJYjV2yxKM4lwZTM/iYDoTlDObGEMi3srYSNqKYMbTo1G4K//PJfEpy5l65/6zWaV2UaVTiCYzgFH86hCTfQggAYDOEJXuDVkc6z8+a8L1orTjlzCL/gfHwDuOeM8g==</latexit><latexit sha1_base64="k5fPkdaDn8Mbouceg63xrCwZPqA=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0i8qLeiF48VjS20oWy2m3bpZhN2J0IJ/QlePKh49R9589+4bXPQ6oOBx3szzMyLMikMet6XU1lZXVvfqG7WtrZ3dvfq+wcPJs014wFLZao7ETVcCsUDFCh5J9OcJpHk7Wh8PfPbj1wbkap7nGQ8TOhQiVgwila6c123X294rjcH+Uv8kjSgRKtf/+wNUpYnXCGT1Jiu72UYFlSjYJJPa73c8IyyMR3yrqWKJtyExfzUKTmxyoDEqbalkMzVnxMFTYyZJJHtTCiOzLI3E//zujnGF2EhVJYjV2yxKM4lwZTM/iYDoTlDObGEMi3srYSNqKYMbTo1G4K//PJfEpy5l65/6zWaV2UaVTiCYzgFH86hCTfQggAYDOEJXuDVkc6z8+a8L1orTjlzCL/gfHwDuOeM8g==</latexit>

v2<latexit sha1_base64="RnLauIjsfIi1c/EKrcB2wuxx9a8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">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</latexit>

vn<latexit sha1_base64="UDpd3tQ+yC7OjOCli3gnCSKnlnY=">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</latexit><latexit sha1_base64="UDpd3tQ+yC7OjOCli3gnCSKnlnY=">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</latexit><latexit sha1_base64="UDpd3tQ+yC7OjOCli3gnCSKnlnY=">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</latexit><latexit sha1_base64="UDpd3tQ+yC7OjOCli3gnCSKnlnY=">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</latexit>

An :<latexit sha1_base64="N0U59mdByUcq5VU79Kcujj3+iIM=">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</latexit><latexit sha1_base64="N0U59mdByUcq5VU79Kcujj3+iIM=">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</latexit><latexit sha1_base64="N0U59mdByUcq5VU79Kcujj3+iIM=">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</latexit><latexit sha1_base64="N0U59mdByUcq5VU79Kcujj3+iIM=">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</latexit>

R1 :<latexit sha1_base64="DokqHpk8rhwebKGNHv+wwRFLMC8=">AAADXnicvVJdaxNBFJ0mautqbasvgi+DIeCDhN2A+AGFogg+VmtsIRvC3dm72aEzs8vMXeuy5C/4qn/NR/+Js0nUJPXZCwNnzv2cMzcplXQUhj92Ot0bN2/t7t0O7tzdv3dweHT/kysqK3AkClXYiwQcKmlwRJIUXpQWQScKz5PLN63//DNaJwvzkeoSJxpmRmZSALXUh2n0anrYCwfhwvh1EK1Aj63sdHrUeRunhag0GhIKnB tHw5ImDViSQuE8iCuHJYhLmOHYQwMa3aRZDDvnfc+kPCusP4b4gl3PaEA7V+vER2qg3G37WvJfvnFF2YtJI01ZERqxbJRVilPB25fzVFoUpGoPQFjpZ+UiBwuCvD4bXWZYaCRbz4P+egMFJnUCvIhrETHhF7qSKeXHfPgsLGkzp/TyPC19jl3GRENplvcc5Syn4yiSZqOeRYNXotDad2viDLRUdYoZVIrmTeyy37gv/C9L4AqWQkrDz8A4foZWZttlnCfR/S2T/CkTxEmh0lbNfgv+498FfvGi7TW7DkbDwctB9D7snbxebeAee8QesycsYs/ZCXvHTtmICZazr+wb+9752d3t7ncPlqGdnVXOA7Zh3Ye/AN+aGf0=</latexit><latexit sha1_base64="DokqHpk8rhwebKGNHv+wwRFLMC8=">AAADXnicvVJdaxNBFJ0mautqbasvgi+DIeCDhN2A+AGFogg+VmtsIRvC3dm72aEzs8vMXeuy5C/4qn/NR/+Js0nUJPXZCwNnzv2cMzcplXQUhj92Ot0bN2/t7t0O7tzdv3dweHT/kysqK3AkClXYiwQcKmlwRJIUXpQWQScKz5PLN63//DNaJwvzkeoSJxpmRmZSALXUh2n0anrYCwfhwvh1EK1Aj63sdHrUeRunhag0GhIKnB tHw5ImDViSQuE8iCuHJYhLmOHYQwMa3aRZDDvnfc+kPCusP4b4gl3PaEA7V+vER2qg3G37WvJfvnFF2YtJI01ZERqxbJRVilPB25fzVFoUpGoPQFjpZ+UiBwuCvD4bXWZYaCRbz4P+egMFJnUCvIhrETHhF7qSKeXHfPgsLGkzp/TyPC19jl3GRENplvcc5Syn4yiSZqOeRYNXotDad2viDLRUdYoZVIrmTeyy37gv/C9L4AqWQkrDz8A4foZWZttlnCfR/S2T/CkTxEmh0lbNfgv+498FfvGi7TW7DkbDwctB9D7snbxebeAee8QesycsYs/ZCXvHTtmICZazr+wb+9752d3t7ncPlqGdnVXOA7Zh3Ye/AN+aGf0=</latexit><latexit sha1_base64="DokqHpk8rhwebKGNHv+wwRFLMC8=">AAADXnicvVJdaxNBFJ0mautqbasvgi+DIeCDhN2A+AGFogg+VmtsIRvC3dm72aEzs8vMXeuy5C/4qn/NR/+Js0nUJPXZCwNnzv2cMzcplXQUhj92Ot0bN2/t7t0O7tzdv3dweHT/kysqK3AkClXYiwQcKmlwRJIUXpQWQScKz5PLN63//DNaJwvzkeoSJxpmRmZSALXUh2n0anrYCwfhwvh1EK1Aj63sdHrUeRunhag0GhIKnB tHw5ImDViSQuE8iCuHJYhLmOHYQwMa3aRZDDvnfc+kPCusP4b4gl3PaEA7V+vER2qg3G37WvJfvnFF2YtJI01ZERqxbJRVilPB25fzVFoUpGoPQFjpZ+UiBwuCvD4bXWZYaCRbz4P+egMFJnUCvIhrETHhF7qSKeXHfPgsLGkzp/TyPC19jl3GRENplvcc5Syn4yiSZqOeRYNXotDad2viDLRUdYoZVIrmTeyy37gv/C9L4AqWQkrDz8A4foZWZttlnCfR/S2T/CkTxEmh0lbNfgv+498FfvGi7TW7DkbDwctB9D7snbxebeAee8QesycsYs/ZCXvHTtmICZazr+wb+9752d3t7ncPlqGdnVXOA7Zh3Ye/AN+aGf0=</latexit><latexit sha1_base64="DokqHpk8rhwebKGNHv+wwRFLMC8=">AAADXnicvVJdaxNBFJ0mautqbasvgi+DIeCDhN2A+AGFogg+VmtsIRvC3dm72aEzs8vMXeuy5C/4qn/NR/+Js0nUJPXZCwNnzv2cMzcplXQUhj92Ot0bN2/t7t0O7tzdv3dweHT/kysqK3AkClXYiwQcKmlwRJIUXpQWQScKz5PLN63//DNaJwvzkeoSJxpmRmZSALXUh2n0anrYCwfhwvh1EK1Aj63sdHrUeRunhag0GhIKnB tHw5ImDViSQuE8iCuHJYhLmOHYQwMa3aRZDDvnfc+kPCusP4b4gl3PaEA7V+vER2qg3G37WvJfvnFF2YtJI01ZERqxbJRVilPB25fzVFoUpGoPQFjpZ+UiBwuCvD4bXWZYaCRbz4P+egMFJnUCvIhrETHhF7qSKeXHfPgsLGkzp/TyPC19jl3GRENplvcc5Syn4yiSZqOeRYNXotDad2viDLRUdYoZVIrmTeyy37gv/C9L4AqWQkrDz8A4foZWZttlnCfR/S2T/CkTxEmh0lbNfgv+498FfvGi7TW7DkbDwctB9D7snbxebeAee8QesycsYs/ZCXvHTtmICZazr+wb+9752d3t7ncPlqGdnVXOA7Zh3Ye/AN+aGf0=</latexit>

LK(R1) =<latexit sha1_base64="Zzys6vTzSoXTyDzxNFBHsnPMLYQ=">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</latexit><latexit sha1_base64="Zzys6vTzSoXTyDzxNFBHsnPMLYQ=">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</latexit><latexit sha1_base64="Zzys6vTzSoXTyDzxNFBHsnPMLYQ=">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</latexit><latexit sha1_base64="Zzys6vTzSoXTyDzxNFBHsnPMLYQ=">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</latexit>

K[x, x�1]<latexit sha1_base64="hCHYNinRkK5Pkl6URTwIZFi7Gj4=">AAADZXicvVLLihNBFK1JfIytzkPFjQsLQ8DFGLoDoi4GBkUQ3IyMcQbScbhdfTspph5N1W0noclnuNXv8g/8DCsPNcm49kLBqXOfnHuzUklPcfxjq9G8dv3Gze1b0e07d3d29/bvffK2cgJ7wirrzjLwqKTBHklSeFY6BJ0pPM0u3sz8p1/QeWnNR5qUONAwNLKQAihQ/ff98cH4c/0smQ7O91pxJ54bvwqSJWixpR2f7zfeprkVlUZDQoH3/aRb0qAGR1IonEZp5bEEcQFD7AdoQKMf1POZp7wdmJwX1oVniM/Z1YwatPcTnYVIDTTym74Z+S9fv6Li5aCWpqwIjVg0KirFyfKZADyXDgWpSQAgnAyzcjECB4KCTGtdhmg1kptMo/ZqAwUm9wKClisRKeGYLmVOo0PefR6XtJ5TBnkOypDjFjFJV5rFf4RyOKLDJJFmrZ5Dg5fCah261WkBWqpJjgVUiqZ16ovfuC3CsiVwBQshpeEnYDw/QSeLzTI+kOj/lsn+lInSzKp8pmZ7Bv7j7qJweMnmmV0FvW7nVSf5ELeOXi8vcJs9Yk/YU5awF+yIvWPHrMcEs+wr+8a+N342d5oPmg8XoY2tZc59tmbNx78ACp4c+g==</latexit><latexit sha1_base64="hCHYNinRkK5Pkl6URTwIZFi7Gj4=">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</latexit><latexit sha1_base64="hCHYNinRkK5Pkl6URTwIZFi7Gj4=">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</latexit><latexit sha1_base64="hCHYNinRkK5Pkl6URTwIZFi7Gj4=">AAADZXicvVLLihNBFK1JfIytzkPFjQsLQ8DFGLoDoi4GBkUQ3IyMcQbScbhdfTspph5N1W0noclnuNXv8g/8DCsPNcm49kLBqXOfnHuzUklPcfxjq9G8dv3Gze1b0e07d3d29/bvffK2cgJ7wirrzjLwqKTBHklSeFY6BJ0pPM0u3sz8p1/QeWnNR5qUONAwNLKQAihQ/ff98cH4c/0smQ7O91pxJ54bvwqSJWixpR2f7zfeprkVlUZDQoH3/aRb0qAGR1IonEZp5bEEcQFD7AdoQKMf1POZp7wdmJwX1oVniM/Z1YwatPcTnYVIDTTym74Z+S9fv6Li5aCWpqwIjVg0KirFyfKZADyXDgWpSQAgnAyzcjECB4KCTGtdhmg1kptMo/ZqAwUm9wKClisRKeGYLmVOo0PefR6XtJ5TBnkOypDjFjFJV5rFf4RyOKLDJJFmrZ5Dg5fCah261WkBWqpJjgVUiqZ16ovfuC3CsiVwBQshpeEnYDw/QSeLzTI+kOj/lsn+lInSzKp8pmZ7Bv7j7qJweMnmmV0FvW7nVSf5ELeOXi8vcJs9Yk/YU5awF+yIvWPHrMcEs+wr+8a+N342d5oPmg8XoY2tZc59tmbNx78ACp4c+g==</latexit>

Rn :<latexit sha1_base64="Dx7mI0QDG5IEEYpe6I7UDoBSMY8=">AAADXnicvVJdaxNBFJ0mautqbasvgi+DIeCDhN2A+AGFogg+VmtsIRvC3dm72aEzs8vMXeuy5C/4qn/NR/+Js0nUJPXZCwNnzv2cMzcplXQUhj92Ot0bN2/t7t0O7tzdv3dweHT/kysqK3AkClXYiwQcKmlwRJIUXpQWQScKz5PLN63//DNaJwvzkeoSJxpmRmZSALXUh6l5NT3shYNwYfw6iFagx1Z2Oj3qvI3TQlQaDQkFzo 2jYUmTBixJoXAexJXDEsQlzHDsoQGNbtIshp3zvmdSnhXWH0N8wa5nNKCdq3XiIzVQ7rZ9Lfkv37ii7MWkkaasCI1YNsoqxang7ct5Ki0KUrUHIKz0s3KRgwVBXp+NLjMsNJKt50F/vYECkzoBXsS1iJjwC13JlPJjPnwWlrSZU3p5npY+xy5joqE0y3uOcpbTcRRJs1HPosErUWjtuzVxBlqqOsUMKkXzJnbZb9wX/pclcAVLIaXhZ2AcP0Mrs+0yzpPo/pZJ/pQJ4qRQaatmvwX/8e8Cv3jR9ppdB6Ph4OUgeh/2Tl6vNnCPPWKP2RMWsefshL1jp2zEBMvZV/aNfe/87O5297sHy9DOzirnAduw7sNflMEaOg==</latexit><latexit sha1_base64="Dx7mI0QDG5IEEYpe6I7UDoBSMY8=">AAADXnicvVJdaxNBFJ0mautqbasvgi+DIeCDhN2A+AGFogg+VmtsIRvC3dm72aEzs8vMXeuy5C/4qn/NR/+Js0nUJPXZCwNnzv2cMzcplXQUhj92Ot0bN2/t7t0O7tzdv3dweHT/kysqK3AkClXYiwQcKmlwRJIUXpQWQScKz5PLN63//DNaJwvzkeoSJxpmRmZSALXUh6l5NT3shYNwYfw6iFagx1Z2Oj3qvI3TQlQaDQkFzo 2jYUmTBixJoXAexJXDEsQlzHDsoQGNbtIshp3zvmdSnhXWH0N8wa5nNKCdq3XiIzVQ7rZ9Lfkv37ii7MWkkaasCI1YNsoqxang7ct5Ki0KUrUHIKz0s3KRgwVBXp+NLjMsNJKt50F/vYECkzoBXsS1iJjwC13JlPJjPnwWlrSZU3p5npY+xy5joqE0y3uOcpbTcRRJs1HPosErUWjtuzVxBlqqOsUMKkXzJnbZb9wX/pclcAVLIaXhZ2AcP0Mrs+0yzpPo/pZJ/pQJ4qRQaatmvwX/8e8Cv3jR9ppdB6Ph4OUgeh/2Tl6vNnCPPWKP2RMWsefshL1jp2zEBMvZV/aNfe/87O5297sHy9DOzirnAduw7sNflMEaOg==</latexit><latexit sha1_base64="Dx7mI0QDG5IEEYpe6I7UDoBSMY8=">AAADXnicvVJdaxNBFJ0mautqbasvgi+DIeCDhN2A+AGFogg+VmtsIRvC3dm72aEzs8vMXeuy5C/4qn/NR/+Js0nUJPXZCwNnzv2cMzcplXQUhj92Ot0bN2/t7t0O7tzdv3dweHT/kysqK3AkClXYiwQcKmlwRJIUXpQWQScKz5PLN63//DNaJwvzkeoSJxpmRmZSALXUh6l5NT3shYNwYfw6iFagx1Z2Oj3qvI3TQlQaDQkFzo 2jYUmTBixJoXAexJXDEsQlzHDsoQGNbtIshp3zvmdSnhXWH0N8wa5nNKCdq3XiIzVQ7rZ9Lfkv37ii7MWkkaasCI1YNsoqxang7ct5Ki0KUrUHIKz0s3KRgwVBXp+NLjMsNJKt50F/vYECkzoBXsS1iJjwC13JlPJjPnwWlrSZU3p5npY+xy5joqE0y3uOcpbTcRRJs1HPosErUWjtuzVxBlqqOsUMKkXzJnbZb9wX/pclcAVLIaXhZ2AcP0Mrs+0yzpPo/pZJ/pQJ4qRQaatmvwX/8e8Cv3jR9ppdB6Ph4OUgeh/2Tl6vNnCPPWKP2RMWsefshL1jp2zEBMvZV/aNfe/87O5297sHy9DOzirnAduw7sNflMEaOg==</latexit><latexit sha1_base64="Dx7mI0QDG5IEEYpe6I7UDoBSMY8=">AAADXnicvVJdaxNBFJ0mautqbasvgi+DIeCDhN2A+AGFogg+VmtsIRvC3dm72aEzs8vMXeuy5C/4qn/NR/+Js0nUJPXZCwNnzv2cMzcplXQUhj92Ot0bN2/t7t0O7tzdv3dweHT/kysqK3AkClXYiwQcKmlwRJIUXpQWQScKz5PLN63//DNaJwvzkeoSJxpmRmZSALXUh6l5NT3shYNwYfw6iFagx1Z2Oj3qvI3TQlQaDQkFzo 2jYUmTBixJoXAexJXDEsQlzHDsoQGNbtIshp3zvmdSnhXWH0N8wa5nNKCdq3XiIzVQ7rZ9Lfkv37ii7MWkkaasCI1YNsoqxang7ct5Ki0KUrUHIKz0s3KRgwVBXp+NLjMsNJKt50F/vYECkzoBXsS1iJjwC13JlPJjPnwWlrSZU3p5npY+xy5joqE0y3uOcpbTcRRJs1HPosErUWjtuzVxBlqqOsUMKkXzJnbZb9wX/pclcAVLIaXhZ2AcP0Mrs+0yzpPo/pZJ/pQJ4qRQaatmvwX/8e8Cv3jR9ppdB6Ph4OUgeh/2Tl6vNnCPPWKP2RMWsefshL1jp2zEBMvZV/aNfe/87O5297sHy9DOzirnAduw7sNflMEaOg==</latexit>

e1<latexit sha1_base64="Gahtq2xaFc9C2zq3tCEmh3z/KjE=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">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</latexit>

e2<latexit sha1_base64="xE9ulyERTuMwyQLHfAprZLOkFtw=">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</latexit><latexit sha1_base64="xE9ulyERTuMwyQLHfAprZLOkFtw=">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</latexit><latexit sha1_base64="xE9ulyERTuMwyQLHfAprZLOkFtw=">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</latexit><latexit sha1_base64="xE9ulyERTuMwyQLHfAprZLOkFtw=">AAADXXicvVLPb9MwFPZaGKOMscGBAxeLqhIHVMWRxtrDpEkIieNQKZvUVJXjvKTWbCeyXxhR1D+BK/xt3PhTcJYO2gmuPMnS5+/99OcXF0o6DIIfO53uvfu7D/Ye9h7tPz54cnj09JPLSytgKnKV28uYO1DSwBQlKrgsLHAdK7iIr942/ovPYJ3MzUesCphrnhmZSsHRUxNYhIvDfjAMgoAxRhvATt4EHozHo5CNKGtc3vpkbeeLo867KMlFqcGgUNy5GQsLnNfcohQKVr2odFBwccUzmHlouAY3r29mXdGBZxKa5tYfg/SG3cyouXau0rGP1ByX7q6vIf/mm5WYjua1NEWJYETbKC0VxZw2D6eJtCBQVR5wYaWflYolt1ygl2erSwa5BrTVqjfYbKC4SZzgXsONiAjhC17LBJenNDwOCtzOKbw8rwufY9sYFkrT3pcgsyWeMibNVj0LBq5FrrXvVkcp11JVCaS8VLiqI5fe4oHwnyw5VbwVUho64cbRCViZ3i3jPAnuT5n4d5leFOcqadQcNOA//l3PL97tdtF/g2k4HA/Zh6B/Nlpv4B55QV6SV4SRE3JG3pNzMiWCZOQr+Ua+d352d7v73YM2tLOzznlGtqz7/BfgDxn5</latexit>

e3<latexit sha1_base64="KetExAdkYUbpPta+yCqRdCJrCTE=">AAADXXicvVJNbxMxEHUTKCWU0sKBAxeLKBIHFK2DoMmhUiWExLEohFbKRtGsdzaxantX9iwlWuUncIXfxo2fgrdJIangykiWnt98+nmSQitPUfRjp9G8c3f33t791oP9hwePDo8ef/J56SSOZK5zd5GAR60sjkiRxovCIZhE43ly+bb2n39G51VuP9KiwImBmVWZkkCBGuL01fSwHXWjKBJC8BqI4zdRAINBvyf6XNSuYG22trPpUeNdnOayNGhJavB+LHoFTSpwpKTGZSsuPRYgL2GG4wAtGPST6nrWJe8EJuVZ7sKxxK/ZzYwKjPcLk4RIAzT3t301+TffuKSsP6mULUpCK1eNslJzynn9cJ4qh5L0IgCQToVZuZyDA0lBnq0uM8wNklssW53NBhps6iUEDTciYsIvdKVSmp/w3uuooO2cIsjzsgg5bhUjesqu7nNUszmdCKHsVj2HFq9kbkzoVsUZGKUXKWZQalpWsc9ucEeGT1bANayEVJYPwXo+RKey22V8INH/KZP8LtOKk1yntZqdGvzHv2uFxbvZLv5vMOp1B13xIWqf9tcbuMeesefsBRPsmJ2y9+yMjZhkM/aVfWPfGz+bu8395sEqtLGzznnCtqz59BfjBhn6</latexit><latexit sha1_base64="KetExAdkYUbpPta+yCqRdCJrCTE=">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</latexit><latexit sha1_base64="KetExAdkYUbpPta+yCqRdCJrCTE=">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</latexit><latexit sha1_base64="KetExAdkYUbpPta+yCqRdCJrCTE=">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</latexit>

en<latexit sha1_base64="XMkPaGHh9uR358SDNcpSIu0qpAQ=">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</latexit><latexit sha1_base64="XMkPaGHh9uR358SDNcpSIu0qpAQ=">AAADXXicvVLPaxNBFJ4mWmustdWDBy+DIeBBwk6gNjkUCiJ4rMTYQjaEt7Nvk6Ezs8vMW2tY8id41b/Nm3+Ks02qSdGrDwa++d7P+eYlhVaeoujHTqN57/7ug72HrUf7jw+eHB49/eTz0kkcyVzn7jIBj1pZHJEijZeFQzCJxovk6m3tv/iMzqvcfqRFgRMDM6syJYECNcSpnR62o24URUIIXgNx8iYKYDDo90Sfi9oVrM3Wdj49aryL01yWBi1JDd6PRa+gSQWOlNS4bMWlxwLkFcxwHKAFg35S3cy65J3ApDzLXTiW+A27mVGB8X5hkhBpgOb+rq8m/+Ybl5T1J5WyRUlo5apRVmpOOa8fzlPlUJJeBADSqTArl3NwICnIs9VlhrlBcotlq7PZQINNvYSg4UZETPiFrlVK81PeO44K2s4pgjyvi5DjVjGip+zqPkc1m9OpEMpu1XNo8VrmxoRuVZyBUXqRYgalpmUV++wWd2T4ZAVcw0pIZfkQrOdDdCq7W8YHEv2fMsnvMq04yXVaq9mpwX/8u1ZYvNvt4v8Go1530BUfovZZf72Be+wFe8leMcFO2Bl7z87ZiEk2Y1/ZN/a98bO529xvHqxCGzvrnGdsy5rPfwGSAho1</latexit><latexit sha1_base64="XMkPaGHh9uR358SDNcpSIu0qpAQ=">AAADXXicvVLPaxNBFJ4mWmustdWDBy+DIeBBwk6gNjkUCiJ4rMTYQjaEt7Nvk6Ezs8vMW2tY8id41b/Nm3+Ks02qSdGrDwa++d7P+eYlhVaeoujHTqN57/7ug72HrUf7jw+eHB49/eTz0kkcyVzn7jIBj1pZHJEijZeFQzCJxovk6m3tv/iMzqvcfqRFgRMDM6syJYECNcSpnR62o24URUIIXgNx8iYKYDDo90Sfi9oVrM3Wdj49aryL01yWBi1JDd6PRa+gSQWOlNS4bMWlxwLkFcxwHKAFg35S3cy65J3ApDzLXTiW+A27mVGB8X5hkhBpgOb+rq8m/+Ybl5T1J5WyRUlo5apRVmpOOa8fzlPlUJJeBADSqTArl3NwICnIs9VlhrlBcotlq7PZQINNvYSg4UZETPiFrlVK81PeO44K2s4pgjyvi5DjVjGip+zqPkc1m9OpEMpu1XNo8VrmxoRuVZyBUXqRYgalpmUV++wWd2T4ZAVcw0pIZfkQrOdDdCq7W8YHEv2fMsnvMq04yXVaq9mpwX/8u1ZYvNvt4v8Go1530BUfovZZf72Be+wFe8leMcFO2Bl7z87ZiEk2Y1/ZN/a98bO529xvHqxCGzvrnGdsy5rPfwGSAho1</latexit><latexit sha1_base64="XMkPaGHh9uR358SDNcpSIu0qpAQ=">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</latexit>

LK(Rn) =<latexit sha1_base64="q0uWc4unfgwiC74hsAGrpmzKbTk=">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</latexit><latexit sha1_base64="q0uWc4unfgwiC74hsAGrpmzKbTk=">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</latexit><latexit sha1_base64="q0uWc4unfgwiC74hsAGrpmzKbTk=">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</latexit><latexit sha1_base64="q0uWc4unfgwiC74hsAGrpmzKbTk=">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</latexit>

LK(1, n)<latexit sha1_base64="foWPRLayAPGV8TmVp66dQ6mYuDI=">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</latexit><latexit sha1_base64="foWPRLayAPGV8TmVp66dQ6mYuDI=">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</latexit><latexit sha1_base64="foWPRLayAPGV8TmVp66dQ6mYuDI=">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</latexit><latexit sha1_base64="foWPRLayAPGV8TmVp66dQ6mYuDI=">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</latexit>

T :<latexit sha1_base64="muEvbV452wrv0l0LzauhpBhk0bE=">AAADXHicvVJbaxNBFJ4mVuvWaqvgiy+DIeCDhN1A8QKFogg+VtvYQjaUs7Nns0PnssyctYYl/8BX/W8++VecXNQk9dkDA9985zrfnKxS0lMc/9hqtW9t376zczfavbd3/8H+wcNP3tZO4EBYZd1FBh6VNDggSQovKoegM4Xn2dXbmf/8MzovrTmjSYUjDWMjCymAAvXx7PXlfifuxXPjN0GyBB22tJPLg9a7NLei1mhIKPB+mP QrGjXgSAqF0yitPVYgrmCMwwANaPSjZj7qlHcDk/PCunAM8Tm7mtGA9n6isxCpgUq/6ZuR//INaypejhppqprQiEWjolacLJ+9m+fSoSA1CQCEk2FWLkpwICios9ZljFYjuck06q42UGByLyBIuBKREn6ha5lTecT7h3FF6zlVkOd5FXLcIibpS7O4lyjHJR0liTRr9RwavBZW69CtSQvQUk1yLKBWNG1SX/zGXRH+WAJXsBBSGn4KxvNTdLLYLOMDif5vmexPmSjNrMpnanZn4D/+XRQWL9lcs5tg0O+96iUf4s7xm+UG7rAn7Cl7xhL2gh2z9+yEDZhgBfvKvrHvrZ/t7fZue28R2tpa5jxia9Z+/AvsNRlb</latexit><latexit sha1_base64="muEvbV452wrv0l0LzauhpBhk0bE=">AAADXHicvVJbaxNBFJ4mVuvWaqvgiy+DIeCDhN1A8QKFogg+VtvYQjaUs7Nns0PnssyctYYl/8BX/W8++VecXNQk9dkDA9985zrfnKxS0lMc/9hqtW9t376zczfavbd3/8H+wcNP3tZO4EBYZd1FBh6VNDggSQovKoegM4Xn2dXbmf/8MzovrTmjSYUjDWMjCymAAvXx7PXlfifuxXPjN0GyBB22tJPLg9a7NLei1mhIKPB+mP QrGjXgSAqF0yitPVYgrmCMwwANaPSjZj7qlHcDk/PCunAM8Tm7mtGA9n6isxCpgUq/6ZuR//INaypejhppqprQiEWjolacLJ+9m+fSoSA1CQCEk2FWLkpwICios9ZljFYjuck06q42UGByLyBIuBKREn6ha5lTecT7h3FF6zlVkOd5FXLcIibpS7O4lyjHJR0liTRr9RwavBZW69CtSQvQUk1yLKBWNG1SX/zGXRH+WAJXsBBSGn4KxvNTdLLYLOMDif5vmexPmSjNrMpnanZn4D/+XRQWL9lcs5tg0O+96iUf4s7xm+UG7rAn7Cl7xhL2gh2z9+yEDZhgBfvKvrHvrZ/t7fZue28R2tpa5jxia9Z+/AvsNRlb</latexit><latexit sha1_base64="muEvbV452wrv0l0LzauhpBhk0bE=">AAADXHicvVJbaxNBFJ4mVuvWaqvgiy+DIeCDhN1A8QKFogg+VtvYQjaUs7Nns0PnssyctYYl/8BX/W8++VecXNQk9dkDA9985zrfnKxS0lMc/9hqtW9t376zczfavbd3/8H+wcNP3tZO4EBYZd1FBh6VNDggSQovKoegM4Xn2dXbmf/8MzovrTmjSYUjDWMjCymAAvXx7PXlfifuxXPjN0GyBB22tJPLg9a7NLei1mhIKPB+mP QrGjXgSAqF0yitPVYgrmCMwwANaPSjZj7qlHcDk/PCunAM8Tm7mtGA9n6isxCpgUq/6ZuR//INaypejhppqprQiEWjolacLJ+9m+fSoSA1CQCEk2FWLkpwICios9ZljFYjuck06q42UGByLyBIuBKREn6ha5lTecT7h3FF6zlVkOd5FXLcIibpS7O4lyjHJR0liTRr9RwavBZW69CtSQvQUk1yLKBWNG1SX/zGXRH+WAJXsBBSGn4KxvNTdLLYLOMDif5vmexPmSjNrMpnanZn4D/+XRQWL9lcs5tg0O+96iUf4s7xm+UG7rAn7Cl7xhL2gh2z9+yEDZhgBfvKvrHvrZ/t7fZue28R2tpa5jxia9Z+/AvsNRlb</latexit><latexit sha1_base64="muEvbV452wrv0l0LzauhpBhk0bE=">AAADXHicvVJbaxNBFJ4mVuvWaqvgiy+DIeCDhN1A8QKFogg+VtvYQjaUs7Nns0PnssyctYYl/8BX/W8++VecXNQk9dkDA9985zrfnKxS0lMc/9hqtW9t376zczfavbd3/8H+wcNP3tZO4EBYZd1FBh6VNDggSQovKoegM4Xn2dXbmf/8MzovrTmjSYUjDWMjCymAAvXx7PXlfifuxXPjN0GyBB22tJPLg9a7NLei1mhIKPB+mP QrGjXgSAqF0yitPVYgrmCMwwANaPSjZj7qlHcDk/PCunAM8Tm7mtGA9n6isxCpgUq/6ZuR//INaypejhppqprQiEWjolacLJ+9m+fSoSA1CQCEk2FWLkpwICios9ZljFYjuck06q42UGByLyBIuBKREn6ha5lTecT7h3FF6zlVkOd5FXLcIibpS7O4lyjHJR0liTRr9RwavBZW69CtSQvQUk1yLKBWNG1SX/zGXRH+WAJXsBBSGn4KxvNTdLLYLOMDif5vmexPmSjNrMpnanZn4D/+XRQWL9lcs5tg0O+96iUf4s7xm+UG7rAn7Cl7xhL2gh2z9+yEDZhgBfvKvrHvrZ/t7fZue28R2tpa5jxia9Z+/AvsNRlb</latexit>

LK(T ) =<latexit sha1_base64="dI9YrAtMOnmA3ojpf87X18zrxZU=">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</latexit><latexit sha1_base64="dI9YrAtMOnmA3ojpf87X18zrxZU=">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</latexit><latexit sha1_base64="dI9YrAtMOnmA3ojpf87X18zrxZU=">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</latexit><latexit sha1_base64="dI9YrAtMOnmA3ojpf87X18zrxZU=">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</latexit>

KhX,Y |XY = 1i<latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="X+n3Rp8U7Dfa3Z8kZ0AhjfisSqg=">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</latexit><latexit sha1_base64="5u8cwuk5oBD+45TWqvxqJF7dwGw=">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</latexit><latexit sha1_base64="5u8cwuk5oBD+45TWqvxqJF7dwGw=">AAADaXicvVJNixNBEO1N/FjHVbOeBBEalwEPS5gJiHoICCIIXlbWuFkyIdT01CTNdvcM3TWuYYy/xqv+H3+JV3uSqEnWswUNr159db+utFTSURT92Gu1r12/cXP/VnD74M7de53Dgw+uqKzAgShUYYcpOFTS4IAkKRyWFkGnCs/Si1dN/OwjWicL857mJY41TI3MpQDy1KTz4G2iwEwV8uHx+efheT9O7NKfdI6ibrQ0fhXEa3DE1nYyOWy9TrJCVBoNCQXOjeJeSeMaLEmhcBEklcMSxAVMceShAY1uXC+fsOChZzKeF9YfQ3zJblbUoJ2b69RnaqCZ24015L9io4ry5+NamrIiNGI1KK8Up4I3evBMWhSk5h6AsNLflYsZWBDkVduaMsVCI9n5Igg3B3j5MifAS7uRkRB+okuZ0azPe0+jkrZrSi/Pcelr7Con7kmz8mcopzPqx7E0W/0sGrwUhdZ+Wp3koKWaZ5hDpWhRJy7/jUPh/14CV7ASUhp+CsbxU7Qy323jPInub5v0T5sgSQuVNWqGDfiPfxf4xYt31+wqGPS6L7rxu4jts4fsMXvCYvaMvWRv2AkbMMG+sK/sG/ve+tl+1F7vaGtvvar32Za1w19iFSGE</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">AAADdHicvVJLixNBEO7N+FjjK6sXQYTGEPCwhJmAqIfAogiCl5U1bpZMCDU9NUmz3T1Dd43rMMZf41X/j7/Eq52HmmQ9W9Dw1Vev7q8rKZR0FIY/9hrBlavXru/faN68dfvO3dbBvQ8uL63AgchVbocJOFTS4IAkKRwWFkEnCk+T81eL+OlHtE7m5j1VBY41TI3MpADy1KT14G2swEwV8uHh2efhWT+K7dKftNphN1wavwyiNWiztR1PDhqv4zQXpUZDQoFzo6hX0LgGS1IonDfj0mEB4hymOPLQgEY3rpdPmPOOZ1Ke5dYfQ3zJblbUoJ2rdOIzNdDM7cYW5L9io5Ky5+NamqIkNGI1KCsVp5wv9OCptChIVR6AsNLflYsZWBDkVduaMsVcI9lq3uxsDvDypU6Al3YjIyb8RBcypVmf956GBW3XFF6ew8LX2FVO1JNm5c9QTmfUjyJptvpZNHghcq39tDrOQEtVpZhBqWhexy77jTvC/70ErmAlpDT8BIzjJ2hlttvGeRLd3zbJnzbNOMlVulCzswD/8e+afvGi3TW7DAa97otu9C5sH71cb+A+e8gesycsYs/YEXvDjtmACfaFfWXf2PfGz+BR0A46q9TG3rrmPtuyoPsL5JAiYQ==</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">AAADdHicvVJLixNBEO7N+FjjK6sXQYTGEPCwhJmAqIfAogiCl5U1bpZMCDU9NUmz3T1Dd43rMMZf41X/j7/Eq52HmmQ9W9Dw1Vev7q8rKZR0FIY/9hrBlavXru/faN68dfvO3dbBvQ8uL63AgchVbocJOFTS4IAkKRwWFkEnCk+T81eL+OlHtE7m5j1VBY41TI3MpADy1KT14G2swEwV8uHh2efhWT+K7dKftNphN1wavwyiNWiztR1PDhqv4zQXpUZDQoFzo6hX0LgGS1IonDfj0mEB4hymOPLQgEY3rpdPmPOOZ1Ke5dYfQ3zJblbUoJ2rdOIzNdDM7cYW5L9io5Ky5+NamqIkNGI1KCsVp5wv9OCptChIVR6AsNLflYsZWBDkVduaMsVcI9lq3uxsDvDypU6Al3YjIyb8RBcypVmf956GBW3XFF6ew8LX2FVO1JNm5c9QTmfUjyJptvpZNHghcq39tDrOQEtVpZhBqWhexy77jTvC/70ErmAlpDT8BIzjJ2hlttvGeRLd3zbJnzbNOMlVulCzswD/8e+afvGi3TW7DAa97otu9C5sH71cb+A+e8gesycsYs/YEXvDjtmACfaFfWXf2PfGz+BR0A46q9TG3rrmPtuyoPsL5JAiYQ==</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit>

Main Examples

v1<latexit sha1_base64="8PAKmmixM9V7EuJjn4WJYmj2zAM=">AAADXXicvVJNb9NAEN0mUEoopS0HDlxWVJE4oMhOsWgOlSo+JI5FIbRSEkXj9ThZdXdt7Y5bIis/gSv8FY78DW78FNYxhaSCKyNZen4z82b37cS5ko6C4PtGo3nr9uadrbute9v3dx7s7u1/cFlhBQ5EpjJ7HoNDJQ0OSJLC89wi6FjhWXzxqsqfXaJ1MjPvaZ7jWMPUyFQKIE/1LyfhZPcg6ARRLwoDHnSiIOwdVqDXO3oeRTzsBMs4ONn/+vobY+x0std4M0oyUWg0JBQ4Nwy7OY1LsCSFwkVrVDjMQVzAFIceGtDoxuXyrAve9kzC08z6zxBfsqsdJWjn5jr2lRpo5m7mKvJvuWFB6dG4lCYvCI2oB6WF4pTx6uI8kRYFqbkHIKz0Z+ViBhYEeXta7dUxU8w0kp2vX0WBSZwA7+FqAeFHupIJzY55NwpyWlMa5t6eZ7nvsXVN2JWm/p+hnM7oOAylWdOzaPBKZFr7aeUoBS3VPMEUCkWLcuTSa9wW/pElcAW1kdLwPhjH+2hlelPGeRLdH5n4t0xrFGcqqdxsV+A/vl3LL971dvF/g0G30+sE7/wCvmR1bLHH7Al7ykL2gp2wt+yUDZhgU/aJfWZfGj+am83t5k5d2tj41fOQrUXz0U8TKBw4</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">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</latexit>

...<latexit sha1_base64="k5fPkdaDn8Mbouceg63xrCwZPqA=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0i8qLeiF48VjS20oWy2m3bpZhN2J0IJ/QlePKh49R9589+4bXPQ6oOBx3szzMyLMikMet6XU1lZXVvfqG7WtrZ3dvfq+wcPJs014wFLZao7ETVcCsUDFCh5J9OcJpHk7Wh8PfPbj1wbkap7nGQ8TOhQiVgwila6c123X294rjcH+Uv8kjSgRKtf/+wNUpYnXCGT1Jiu72UYFlSjYJJPa73c8IyyMR3yrqWKJtyExfzUKTmxyoDEqbalkMzVnxMFTYyZJJHtTCiOzLI3E//zujnGF2EhVJYjV2yxKM4lwZTM/iYDoTlDObGEMi3srYSNqKYMbTo1G4K//PJfEpy5l65/6zWaV2UaVTiCYzgFH86hCTfQggAYDOEJXuDVkc6z8+a8L1orTjlzCL/gfHwDuOeM8g==</latexit><latexit sha1_base64="k5fPkdaDn8Mbouceg63xrCwZPqA=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0i8qLeiF48VjS20oWy2m3bpZhN2J0IJ/QlePKh49R9589+4bXPQ6oOBx3szzMyLMikMet6XU1lZXVvfqG7WtrZ3dvfq+wcPJs014wFLZao7ETVcCsUDFCh5J9OcJpHk7Wh8PfPbj1wbkap7nGQ8TOhQiVgwila6c123X294rjcH+Uv8kjSgRKtf/+wNUpYnXCGT1Jiu72UYFlSjYJJPa73c8IyyMR3yrqWKJtyExfzUKTmxyoDEqbalkMzVnxMFTYyZJJHtTCiOzLI3E//zujnGF2EhVJYjV2yxKM4lwZTM/iYDoTlDObGEMi3srYSNqKYMbTo1G4K//PJfEpy5l65/6zWaV2UaVTiCYzgFH86hCTfQggAYDOEJXuDVkc6z8+a8L1orTjlzCL/gfHwDuOeM8g==</latexit><latexit sha1_base64="k5fPkdaDn8Mbouceg63xrCwZPqA=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0i8qLeiF48VjS20oWy2m3bpZhN2J0IJ/QlePKh49R9589+4bXPQ6oOBx3szzMyLMikMet6XU1lZXVvfqG7WtrZ3dvfq+wcPJs014wFLZao7ETVcCsUDFCh5J9OcJpHk7Wh8PfPbj1wbkap7nGQ8TOhQiVgwila6c123X294rjcH+Uv8kjSgRKtf/+wNUpYnXCGT1Jiu72UYFlSjYJJPa73c8IyyMR3yrqWKJtyExfzUKTmxyoDEqbalkMzVnxMFTYyZJJHtTCiOzLI3E//zujnGF2EhVJYjV2yxKM4lwZTM/iYDoTlDObGEMi3srYSNqKYMbTo1G4K//PJfEpy5l65/6zWaV2UaVTiCYzgFH86hCTfQggAYDOEJXuDVkc6z8+a8L1orTjlzCL/gfHwDuOeM8g==</latexit><latexit sha1_base64="k5fPkdaDn8Mbouceg63xrCwZPqA=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0i8qLeiF48VjS20oWy2m3bpZhN2J0IJ/QlePKh49R9589+4bXPQ6oOBx3szzMyLMikMet6XU1lZXVvfqG7WtrZ3dvfq+wcPJs014wFLZao7ETVcCsUDFCh5J9OcJpHk7Wh8PfPbj1wbkap7nGQ8TOhQiVgwila6c123X294rjcH+Uv8kjSgRKtf/+wNUpYnXCGT1Jiu72UYFlSjYJJPa73c8IyyMR3yrqWKJtyExfzUKTmxyoDEqbalkMzVnxMFTYyZJJHtTCiOzLI3E//zujnGF2EhVJYjV2yxKM4lwZTM/iYDoTlDObGEMi3srYSNqKYMbTo1G4K//PJfEpy5l65/6zWaV2UaVTiCYzgFH86hCTfQggAYDOEJXuDVkc6z8+a8L1orTjlzCL/gfHwDuOeM8g==</latexit>

v2<latexit sha1_base64="RnLauIjsfIi1c/EKrcB2wuxx9a8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">AAADXXicvVLNbtNAEN4mUEoopT8HDlxWVJEQQpEdsGgOlSp+JI5FIbRSEkXj9ThZdXdt7Y5bIquPwBWegTfgMbhy41FYxxSSCq6MZOnzNzPf7H47ca6koyD4vtZo3ri5fmvjduvO5t2te9s7u+9dVliBA5GpzJ7G4FBJgwOSpPA0twg6VngSn72s8ifnaJ3MzDua5zjWMDUylQLIU/3zSXeyvR90gqgXhQEPOlEQ9p5WoNc7eBZFPOwEi9g/2v366tvel8fHk53G61GSiUKjIaHAuWHYzWlcgiUpFF62RoXDHMQZTHHooQGNblwuznrJ255JeJpZ/xniC3a5owTt3FzHvlIDzdz1XEX+LTcsKD0Yl9LkBaER9aC0UJwyXl2cJ9KiIDX3AISV/qxczMCCIG9Pq708ZoqZRrLz1asoMIkT4D1cLiD8QBcyodkh70ZBTitKw9zb8yT3PbauCbvS1P8zlNMZHYahNCt6Fg1eiExrP60cpaClmieYQqHoshy59Aq3hX9kCVxBbaQ0vA/G8T5amV6XcZ5E90cm/i3TGsWZSio32xX4j2/X8ot3tV3832DQ7fQ6wVu/gC9YHRvsAXvIHrGQPWdH7A07ZgMm2JR9ZJ/Y58aP5npzs7lVlzbWfvXssZVo3v8Jw2wdLw==</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">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</latexit>

AN :<latexit sha1_base64="vU5DVyg2wwR/q9yIIIzJ1YgS/+g=">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</latexit><latexit sha1_base64="h0HpPCyrm5mzQnmyXEXB6cDUCrI=">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</latexit><latexit sha1_base64="h0HpPCyrm5mzQnmyXEXB6cDUCrI=">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</latexit><latexit sha1_base64="GIBnNZXFR/3o7X0kVP/tprKa4J0=">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</latexit> v3

<latexit sha1_base64="wP3kMGOAlqwZ2s3wqBWzeqfvExI=">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</latexit><latexit sha1_base64="wP3kMGOAlqwZ2s3wqBWzeqfvExI=">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</latexit><latexit sha1_base64="wP3kMGOAlqwZ2s3wqBWzeqfvExI=">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</latexit><latexit sha1_base64="wP3kMGOAlqwZ2s3wqBWzeqfvExI=">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</latexit>

LK(AN) =<latexit sha1_base64="7mK/1stv83V2k5IpyFs/CqCo9dU=">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</latexit><latexit sha1_base64="7mK/1stv83V2k5IpyFs/CqCo9dU=">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</latexit><latexit sha1_base64="7mK/1stv83V2k5IpyFs/CqCo9dU=">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</latexit><latexit sha1_base64="7mK/1stv83V2k5IpyFs/CqCo9dU=">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</latexit>

FMN(K)<latexit sha1_base64="mA9TdQ9YKCZXgH3oBdfQpXEcigQ=">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</latexit><latexit sha1_base64="mA9TdQ9YKCZXgH3oBdfQpXEcigQ=">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</latexit><latexit sha1_base64="mA9TdQ9YKCZXgH3oBdfQpXEcigQ=">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</latexit><latexit sha1_base64="mA9TdQ9YKCZXgH3oBdfQpXEcigQ=">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</latexit>

Page 7: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Properties of Leavitt path algebrasLK(E)

<latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">AAADYHicvVJbaxNBFJ4mXtp4aaNv+jIYAhUkZIOiPhSKUhD0oVLTFrIhnJ09m512ZnaZOWsNS/6Dr/rPfPaPOJuNmqQ+e2Dgm+9c55sT5Uo66vd/bDWaN27eur2907pz99793b32g1OXFVbgUGQqs+cROFTS4JAkKTzPLYKOFJ5Fl28r/9lntE5m5hPNchxrmBqZSAHkqdMPk/f7R08ne51+r78wfh0ES9BhSzuetBtHYZyJQq MhocC5UTDIaVyCJSkUzlth4TAHcQlTHHloQKMbl4tx57zrmZgnmfXHEF+wqxklaOdmOvKRGih1m76K/JdvVFDyalxKkxeERtSNkkJxynj1dh5Li4LUzAMQVvpZuUjBgiCv0FqXKWYayc7mre5qAwUmdgK8jCsRIeEXupIxpQd88KKf03pO7uV5lvscW8cEA2nqe4pymtJBEEizVs+iwSuRae27lWECWqpZjAkUiuZl6JLfuCv8P0vgCmohpeEnYBw/QSuTzTLOk+j+lon+lGmFUabiSs1uBf7j37X84gWba3YdDAe9173g4/PO4ZvlBm6zx+wJ22cBe8kO2Tt2zIZMsAv2lX1j3xs/mzvN3Wa7Dm1sLXMesjVrPvoFfE0ahQ==</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">AAADYHicvVJbaxNBFJ4mXtp4aaNv+jIYAhUkZIOiPhSKUhD0oVLTFrIhnJ09m512ZnaZOWsNS/6Dr/rPfPaPOJuNmqQ+e2Dgm+9c55sT5Uo66vd/bDWaN27eur2907pz99793b32g1OXFVbgUGQqs+cROFTS4JAkKTzPLYKOFJ5Fl28r/9lntE5m5hPNchxrmBqZSAHkqdMPk/f7R08ne51+r78wfh0ES9BhSzuetBtHYZyJQq MhocC5UTDIaVyCJSkUzlth4TAHcQlTHHloQKMbl4tx57zrmZgnmfXHEF+wqxklaOdmOvKRGih1m76K/JdvVFDyalxKkxeERtSNkkJxynj1dh5Li4LUzAMQVvpZuUjBgiCv0FqXKWYayc7mre5qAwUmdgK8jCsRIeEXupIxpQd88KKf03pO7uV5lvscW8cEA2nqe4pymtJBEEizVs+iwSuRae27lWECWqpZjAkUiuZl6JLfuCv8P0vgCmohpeEnYBw/QSuTzTLOk+j+lon+lGmFUabiSs1uBf7j37X84gWba3YdDAe9173g4/PO4ZvlBm6zx+wJ22cBe8kO2Tt2zIZMsAv2lX1j3xs/mzvN3Wa7Dm1sLXMesjVrPvoFfE0ahQ==</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">AAADYHicvVJbaxNBFJ4mXtp4aaNv+jIYAhUkZIOiPhSKUhD0oVLTFrIhnJ09m512ZnaZOWsNS/6Dr/rPfPaPOJuNmqQ+e2Dgm+9c55sT5Uo66vd/bDWaN27eur2907pz99793b32g1OXFVbgUGQqs+cROFTS4JAkKTzPLYKOFJ5Fl28r/9lntE5m5hPNchxrmBqZSAHkqdMPk/f7R08ne51+r78wfh0ES9BhSzuetBtHYZyJQq MhocC5UTDIaVyCJSkUzlth4TAHcQlTHHloQKMbl4tx57zrmZgnmfXHEF+wqxklaOdmOvKRGih1m76K/JdvVFDyalxKkxeERtSNkkJxynj1dh5Li4LUzAMQVvpZuUjBgiCv0FqXKWYayc7mre5qAwUmdgK8jCsRIeEXupIxpQd88KKf03pO7uV5lvscW8cEA2nqe4pymtJBEEizVs+iwSuRae27lWECWqpZjAkUiuZl6JLfuCv8P0vgCmohpeEnYBw/QSuTzTLOk+j+lon+lGmFUabiSs1uBf7j37X84gWba3YdDAe9173g4/PO4ZvlBm6zx+wJ22cBe8kO2Tt2zIZMsAv2lX1j3xs/mzvN3Wa7Dm1sLXMesjVrPvoFfE0ahQ==</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">AAADYHicvVJbaxNBFJ4mXtp4aaNv+jIYAhUkZIOiPhSKUhD0oVLTFrIhnJ09m512ZnaZOWsNS/6Dr/rPfPaPOJuNmqQ+e2Dgm+9c55sT5Uo66vd/bDWaN27eur2907pz99793b32g1OXFVbgUGQqs+cROFTS4JAkKTzPLYKOFJ5Fl28r/9lntE5m5hPNchxrmBqZSAHkqdMPk/f7R08ne51+r78wfh0ES9BhSzuetBtHYZyJQq MhocC5UTDIaVyCJSkUzlth4TAHcQlTHHloQKMbl4tx57zrmZgnmfXHEF+wqxklaOdmOvKRGih1m76K/JdvVFDyalxKkxeERtSNkkJxynj1dh5Li4LUzAMQVvpZuUjBgiCv0FqXKWYayc7mre5qAwUmdgK8jCsRIeEXupIxpQd88KKf03pO7uV5lvscW8cEA2nqe4pymtJBEEizVs+iwSuRae27lWECWqpZjAkUiuZl6JLfuCv8P0vgCmohpeEnYBw/QSuTzTLOk+j+lon+lGmFUabiSs1uBf7j37X84gWba3YdDAe9173g4/PO4ZvlBm6zx+wJ22cBe8kO2Tt2zIZMsAv2lX1j3xs/mzvN3Wa7Dm1sLXMesjVrPvoFfE0ahQ==</latexit>

has some specified algebraic property ,<latexit sha1_base64="OwMCur3qmPySI1+hun+S5yN74SQ=">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</latexit><latexit sha1_base64="A/SSRLWZJnEcRYFSpSXJCCdRBBw=">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</latexit><latexit sha1_base64="A/SSRLWZJnEcRYFSpSXJCCdRBBw=">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</latexit><latexit sha1_base64="0fewRy088rpzYS2OMGBR5OZWFso=">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</latexit>

E<latexit sha1_base64="FKJjd8xw0DoagSjQqfenD04oLjA=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">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</latexit><latexit sha1_base64="M0ROzkQIVaOvJ4omKdKT8tj4tXc=">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</latexit> has some specified graph-theoretic property

finite dimensional finite and acyclic

LK(E)<latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit>

E<latexit sha1_base64="FKJjd8xw0DoagSjQqfenD04oLjA=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">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</latexit><latexit sha1_base64="M0ROzkQIVaOvJ4omKdKT8tj4tXc=">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</latexit>

e5<latexit sha1_base64="2oTVAYPOXK7qVoTAKdaZt9kQovk=">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</latexit><latexit sha1_base64="fuQ1sFb76il7pyt7uv1eo8bJJpg=">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</latexit><latexit sha1_base64="fuQ1sFb76il7pyt7uv1eo8bJJpg=">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</latexit>

v1<latexit sha1_base64="8PAKmmixM9V7EuJjn4WJYmj2zAM=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">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</latexit>

v2<latexit sha1_base64="RnLauIjsfIi1c/EKrcB2wuxx9a8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">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</latexit>

v3<latexit sha1_base64="aCJXJ5RlxA9vJSXn+kHy1M4mML0=">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</latexit><latexit sha1_base64="7+An/e4ZjGTsSKaG/UAenbk8Nsc=">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</latexit><latexit sha1_base64="7+An/e4ZjGTsSKaG/UAenbk8Nsc=">AAADXXicvVLNbtNAEN4mUIop/T1w4LKiioQQiuwUi+ZQqeJH4lgUQivFUbRej51Vd9fW7rglsvIIXOEZeAMegys3HoV1TCGp4MpIlj5/M/PN7rcTF1JY9P3va632rdvrdzbuevc2729t7+zuvbd5aTgMeS5zcx4zC1JoGKJACeeFAaZiCWfxxcs6f3YJxopcv8NZAWPFMi1SwRk6anA5OZzsHPhdP+yHgU/9bugH/cMa9PtHz8KQBl1/EQcne19ffdv/8uR0stt6HSU5LxVo5JJZOwp6BY4rZlBwCXMvKi0UjF+wDEYOaqbAjqvFWee045iEprlxn0a6YJc7KqasnanYVSqGU3szV5N/y41KTI/GldBFiaB5MygtJcWc1heniTDAUc4cYNwId1bKp8wwjs4er7M8JoNcAZrZ6lUk04nlzHm4XIDwAa9EgtNj2gv9AleURoWz52nhekxTE/SEbv6nILIpHgeB0Ct6BjRc8VwpN62KUqaEnCWQslLivIpseo073D2yYFSyxkih6YBpSwdgRHpTxjoS7B+Z+LeMF8W5TGo3OzX4j2/nucW73i76bzDsdftd/61bwBekiQ3ykDwij0lAnpMT8oackiHhJCMfySfyufWjvd7ebG81pa21Xz37ZCXaD34CxmMdMA==</latexit>

v4<latexit sha1_base64="5o7IKDY9gLFdRStvBpyGFyzmiOI=">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</latexit><latexit sha1_base64="DY7vSTAraABkoaKhE1CBCXv4ZaE=">AAADXXicvVLNbtNAEN4mUIop/T1w4LKiioQQiuxQi+ZQqeJH4lgUQivFUbRej51Vd9fW7rglsvIIXOEZeAMegys3HoV1TCGp4MpIlj5/M/PN7rcTF1JY9P3va632rdvrdzbuevc2729t7+zuvbd5aTgMeS5zcx4zC1JoGKJACeeFAaZiCWfxxcs6f3YJxopcv8NZAWPFMi1SwRk6anA5OZzsHPhdP+yHgU/9bugH/Wc16PePDsOQBl1/EQcne19ffdv/8uR0stt6HSU5LxVo5JJZOwp6BY4rZlBwCXMvKi0UjF+wDEYOaqbAjqvFWee045iEprlxn0a6YJc7KqasnanYVSqGU3szV5N/y41KTI/GldBFiaB5MygtJcWc1heniTDAUc4cYNwId1bKp8wwjs4er7M8JoNcAZrZ6lUk04nlzHm4XIDwAa9EgtNj2gv9AleURoWz52nhekxTE/SEbv6nILIpHgeB0Ct6BjRc8VwpN62KUqaEnCWQslLivIpseo073D2yYFSyxkih6YBpSwdgRHpTxjoS7B+Z+LeMF8W5TGo3OzX4j2/nucW73i76bzDsdftd/61bwBekiQ3ykDwij0lAnpMT8oackiHhJCMfySfyufWjvd7ebG81pa21Xz37ZCXaD34CyVodMQ==</latexit><latexit sha1_base64="DY7vSTAraABkoaKhE1CBCXv4ZaE=">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</latexit>

v5<latexit sha1_base64="XEnGBwIhIUAc946elKahyxHOr10=">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</latexit><latexit sha1_base64="yaUbGn+TXLSwb/L1QU3Kk9yCgMc=">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</latexit><latexit sha1_base64="yaUbGn+TXLSwb/L1QU3Kk9yCgMc=">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</latexit>

v6<latexit sha1_base64="UfomTyGXDzzJ10RXwIfU4GSYSXE=">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</latexit><latexit sha1_base64="3gg7qt9+5vGUIG1FQwwKinA/wxc=">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</latexit><latexit sha1_base64="3gg7qt9+5vGUIG1FQwwKinA/wxc=">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</latexit>

e2<latexit sha1_base64="+qvft35mNCYBd7mHkko9V+wUF/c=">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</latexit><latexit sha1_base64="4TWgrdRvjtxoRH9cYpisFS/0ZOc=">AAADXXicvVLBbhMxEHUTKCGU0pYDBy4WVSQOKFqvVJocKlVCSEhcikJopWwUeb2ziVXbu7JnaVerfAJX+A++pRdu/AR3vF0KSQVXRlrp7ZuZN/bzxLmSDoPg20arfefu5r3O/e6DrYfbj3Z29z64rLACxiJTmT2LuQMlDYxRooKz3ALXsYLT+PxVnT/9CNbJzLzHMoep5nMjUyk4emoEs3C2sx/0gyBgjNEasMOXgQfD4SBkA8rqlI/9486Pr1dXrbcns93W6yjJRKHBoFDcuQkLc5xW3KIUCpbdqHCQc3HO5zDx0HANblpdn3VJe55JaJpZ/xmk1+xqR8W1c6WOfaXmuHC3czX5t9ykwHQwraTJCwQjmkFpoShmtL44TaQFgar0gAsr/VmpWHDLBXp7ur3VMXPINKAt16+iuEmc4N7D1QKES7yQCS6OaHgQ5LimNMm9PS9y32ObGhZK0/wvQM4XeMSYNGt6FgxciExrP62KUq6lKhNIeaFwWUUuvcE94R9Zcqp4Y6Q0dMSNoyOwMr0t4zwJ7o9M/FumG8WZSmo3ezX4j2/X9Yt3s13032Ac9of94J1fwAFpokOekmfkOWHkkByTN+SEjIkgc/KJfCZfWt/bm+2t9nZT2tr41fOYrEX7yU+6dB3c</latexit><latexit sha1_base64="4TWgrdRvjtxoRH9cYpisFS/0ZOc=">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</latexit>

e1<latexit sha1_base64="Gahtq2xaFc9C2zq3tCEmh3z/KjE=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">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</latexit>

e3<latexit sha1_base64="u6aps99kjMZnFt6LACGZVHxr8GA=">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</latexit><latexit sha1_base64="ko+763tzlQVosGPwibi3OupeYmY=">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</latexit><latexit sha1_base64="ko+763tzlQVosGPwibi3OupeYmY=">AAADXXicvVLBbhMxEHUTKCGU0sKBAxeLKhIHFK2DoMmhUiWEhMSlKIRWSqJo1jubWLW9K3uWEq36CVzhP/iWXrjxE9zxdikkFVwZaaW3b2be2M8T51p5iqJvG43mjZubt1q323e27m7f29m9/95nhZM4kpnO3EkMHrWyOCJFGk9yh2Bijcfx6csqf/wBnVeZfUfLHKcG5lalSgIFaoizZ7OdvagbRZEQgldA7L+IAhgM+j3R56JKhdg7bP34enHReHM02228miSZLAxakhq8H4teTtMSHCmp8bw9KTzmIE9hjuMALRj00/LyrOe8E5iEp5kLnyV+ya52lGC8X5o4VBqghb+eq8i/5cYFpf1pqWxeEFpZD0oLzSnj1cV5ohxK0ssAQDoVzsrlAhxICva0O6tj5pgZJLdcv4oGm3gJwcPVAsKPdKYSWhzw3vMopzWlcR7seZqHHlfXiJ6y9f8C1XxBB0Iou6bn0OKZzIwJ08pJCkbpZYIpFJrOy4lPr3BHhkdWwDXURirLh2A9H6JT6XUZH0j0f2Ti3zLtSZzppHKzU4H/+HbtsHhX28X/DUa97qAbvQ0L2Gd1tNgj9pg9YYLts0P2mh2xEZNszj6xz+xL43tzs7nV3K5LGxu/eh6wtWg+/Am9ax3d</latexit>

e4<latexit sha1_base64="u2R2RalfWEo8fhoEzg7jafnylrE=">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</latexit><latexit sha1_base64="qjGof5nbXTi2LG7wMGqXhXEqGtw=">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</latexit><latexit sha1_base64="qjGof5nbXTi2LG7wMGqXhXEqGtw=">AAADXXicvVLBbhMxEHUTKCGU0sKBAxeLKhIHFK0joMmhUiWEhMSlKIRWSqJo1jubWLW9K3uWEq36CVzhP/iWXrjxE9zxdikkFVwZaaW3b2be2M8T51p5iqJvG43mjZubt1q323e27m7f29m9/95nhZM4kpnO3EkMHrWyOCJFGk9yh2Bijcfx6csqf/wBnVeZfUfLHKcG5lalSgIFaoizZ7OdvagbRZEQgldA7L+IAhgM+j3R56JKhdg7bP34enHReHM02228miSZLAxakhq8H4teTtMSHCmp8bw9KTzmIE9hjuMALRj00/LyrOe8E5iEp5kLnyV+ya52lGC8X5o4VBqghb+eq8i/5cYFpf1pqWxeEFpZD0oLzSnj1cV5ohxK0ssAQDoVzsrlAhxICva0O6tj5pgZJLdcv4oGm3gJwcPVAsKPdKYSWhzw3vMopzWlcR7seZqHHlfXiJ6y9f8C1XxBB0Iou6bn0OKZzIwJ08pJCkbpZYIpFJrOy4lPr3BHhkdWwDXURirLh2A9H6JT6XUZH0j0f2Ti3zLtSZzppHKzU4H/+HbtsHhX28X/DUa97qAbvQ0L2Gd1tNgj9pg9YYLts0P2mh2xEZNszj6xz+xL43tzs7nV3K5LGxu/eh6wtWg+/AnAYh3e</latexit>

e6<latexit sha1_base64="4hpldoBTI3TdciTk2lw/afLqBL4=">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</latexit><latexit sha1_base64="XK6KnUlmY1y/hiZoiu7q7bTAgSU=">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</latexit><latexit sha1_base64="XK6KnUlmY1y/hiZoiu7q7bTAgSU=">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</latexit>

Page 8: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Properties of Leavitt path algebras

simple hereditary saturated subsets are trivial and every cycle has an exit

LK(E)<latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">AAADYHicvVJbaxNBFJ4mXtp4aaNv+jIYAhUkZIOiPhSKUhD0oVLTFrIhnJ09m512ZnaZOWsNS/6Dr/rPfPaPOJuNmqQ+e2Dgm+9c55sT5Uo66vd/bDWaN27eur2907pz99793b32g1OXFVbgUGQqs+cROFTS4JAkKTzPLYKOFJ5Fl28r/9lntE5m5hPNchxrmBqZSAHkqdMPk/f7R08ne51+r78wfh0ES9BhSzuetBtHYZyJQqMhocC5UTDIaVyCJSkUzlth4TAHcQlTHHloQKMbl4tx57zrmZgnmfXHEF+wqxklaOdmOvKRGih1m76K/JdvVFDyalxKkxeERtSNkkJxynj1dh5Li4LUzAMQVvpZuUjBgiCv0FqXKWYayc7mre5qAwUmdgK8jCsRIeEXupIxpQd88KKf03pO7uV5lvscW8cEA2nqe4pymtJBEEizVs+iwSuRae27lWECWqpZjAkUiuZl6JLfuCv8P0vgCmohpeEnYBw/QSuTzTLOk+j+lon+lGmFUabiSs1uBf7j37X84gWba3YdDAe9173g4/PO4ZvlBm6zx+wJ22cBe8kO2Tt2zIZMsAv2lX1j3xs/mzvN3Wa7Dm1sLXMesjVrPvoFfE0ahQ==</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit>

E<latexit sha1_base64="FKJjd8xw0DoagSjQqfenD04oLjA=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">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</latexit><latexit sha1_base64="M0ROzkQIVaOvJ4omKdKT8tj4tXc=">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</latexit>

v<latexit sha1_base64="S52Y8C68YUN59ZYa74Hw/bvPAhc=">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</latexit><latexit sha1_base64="Y/H/pdQD6mwWuQ4XMEcgIAcPm2A=">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</latexit><latexit sha1_base64="Y/H/pdQD6mwWuQ4XMEcgIAcPm2A=">AAADhnicvVJNb9NAEN3GfLThK4UjUrWiioRQFeyA1eZQKQIhcWxVQivFUbRej5NVd9fW7rglsnLkzq9BvcHf4DfwJ1jHBZKUMyNZen4z82b37cS5FBZ9/8dGw7t1+87dza3mvfsPHj5qbT/+aLPCcBjwTGbmLGYWpNAwQIESznIDTMUSTuPzt1X+9AKMFZn+gLMcRopNtEgFZ+iocetFGS1EhmYSj0q/44e9MPD3/E7oB71XFej1Dl6H4fxiPm7tuvwi6E0QXIPd/s7V8c/PO1dH4+3GuyjJeKFAI5fM2mHQzXFUMoOCS5g3o8JCzvg5m8DQQc0U2FG5OM+cth2T0DQz7tNIF+xyR8mUtTMVu0rFcGrXcxX5r9ywwPRgVAqdFwia14PSQlLMaOUQTYQBjnLmAONGuLNSPmWGcXQ+NtvLYyaQKUAzW72KZDqxnDmzlwsQPuGlSHB6SLuhn+OK0jB39uzlrsfUNUFX6Pp/CmIyxcMgEHpFz4CGS54p5aaVUcqUkLMEUlZInJeRTX/jNnfbIBiVrDZSaHrCtKUnYES6LmMdCfavTPxHphnFmUwqN9sV+I9v13SLF6yv2U0w6HZ6neDYLeAbUscmeUqekeckIPukT96TIzIgnHwhX8k38t3b8l56obdflzY2rnuekJXw+r8AisopMA==</latexit><latexit sha1_base64="k1d6eUwxFOvn4dWOMoY+dFgT+YM=">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</latexit>

u<latexit sha1_base64="kYiNsLEMnKqUGhzgoOzbf2u3p7w=">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</latexit><latexit sha1_base64="N6nLa5gxfeCi3/q3y3PikJdne+Q=">AAADhnicvVJNb9NAEN3GfLThoykckaoVVSSEqmAHrDaHShEIiWOrElopjqL1epysuru2dseUyMqRO78G9QZ/g9/An2AdF0hSzoxk6fnNzJvdtxPnUlj0/R8bDe/W7Tt3N7ea9+4/eLjd2nn0wWaF4TDgmczMecwsSKFhgAIlnOcGmIolnMUXb6r82UcwVmT6Pc5yGCk20SIVnKGjxq3nZbQQGZpJPCr9jh/2wsDf9zuhH/ReVqDXO3wVhvNiPm7tufwi6E0QXIO9/u7Vyc/Pu1fH453G2yjJeKFAI5fM2mHQzXFUMoOCS5g3o8JCzvgFm8DQQc0U2FG5OM+cth2T0DQz7tNIF+xyR8mUtTMVu0rFcGrXcxX5r9ywwPRwVAqdFwia14PSQlLMaOUQTYQBjnLmAONGuLNSPmWGcXQ+NtvLYyaQKUAzW72KZDqxnDmzlwsQPuGlSHB6RLuhn+OK0jB39uznrsfUNUFX6Pp/CmIyxaMgEHpFz4CGS54p5aaVUcqUkLMEUlZInJeRTX/jNnfbIBiVrDZSaHrKtKWnYES6LmMdCfavTPxHphnFmUwqN9sV+I9v13SLF6yv2U0w6HZ6neDELeBrUscmeUKekmckIAekT96RYzIgnHwhX8k38t3b8l54oXdQlzY2rnsek5Xw+r8Ah9IpLw==</latexit><latexit sha1_base64="N6nLa5gxfeCi3/q3y3PikJdne+Q=">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</latexit><latexit sha1_base64="U2EiY8yt25I08kr2HkgfCIk4Eeg=">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</latexit>

v 2 V ) u 2 V<latexit sha1_base64="1ctxCmuK/e9T+vzdt+VUW2Nbskk=">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</latexit><latexit sha1_base64="qTuomRrrl99jkZahQ2yo2C2Nn9c=">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</latexit><latexit sha1_base64="qTuomRrrl99jkZahQ2yo2C2Nn9c=">AAADdHicvVJNixNBEO1N/Fjjx2b1IojQGAIeJMwERD0sLorgcXXN7kImLDU9NUmzPd1Dd83GMMb/4V2P+g/8If4Ij+LVnsyqSdazBQOvX1W9mn7Vca6koyD4ttFoXrh46fLmldbVa9dvbLW3bx44U1iBA2GUsUcxOFRS44AkKTzKLUIWKzyMT55X+cNTtE4a/YZmOY4yGGuZSgHkqeP27dNIan4QvZbjCYG1ZsqLBXPc7gS9YBH8PAjPQOfpj08fvr8zX/eOtxsvosSIIkNNQoFzw7Cf06gES1IonLeiwmEO4gTGOPRQQ4ZuVC6uMOddzyQ8NdZ/mviCXe4oIXNulsW+MgOauPVcRf4rNywofTwqpc4LQi3qQWmhOBle+cETaVGQmnkAwkr/r1xMwIIg71qruzxmjCZDsrPVqyjQiRPgrV0uIHxLU5nQZIf3HwY5rSgNc2/Pg9z32Lom7EtdnydYLWInDKVe0bOocSpMlvlpZZRCJtUswRQKRfMyculv3BV+9xK4gtpIv8p90I7vo5XpuozzJLq/MvEfmVYUG5VUbnYr8B931/IPL1x/ZufBoN970gtfBZ3dZ6yOTXaH3WP3WcgesV32ku2xARPsPfvIPrMvjZ/Nu81Os1uXNjbOem6xlWj2fgEBnSfD</latexit><latexit sha1_base64="/v9sxwJNt2JEiIcutsk3UZBfNhA=">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</latexit>

u<latexit sha1_base64="kYiNsLEMnKqUGhzgoOzbf2u3p7w=">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</latexit><latexit sha1_base64="N6nLa5gxfeCi3/q3y3PikJdne+Q=">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</latexit><latexit sha1_base64="N6nLa5gxfeCi3/q3y3PikJdne+Q=">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</latexit><latexit sha1_base64="U2EiY8yt25I08kr2HkgfCIk4Eeg=">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</latexit>

v1<latexit sha1_base64="lEQQ/o44Ri6YZY+XQDtcfweEWG4=">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</latexit><latexit sha1_base64="VMddr955s5n6Rw6J+zJB2A1yElQ=">AAADiHicvVLdatswFFbj/XTpftLtclDESmAXIVjZTOuLQukY7LKly1qIQ5Dl40RUko0ktzMml3uBPU1ut7fYM+wlJsfdlqS73gHD5++c8x3p04lzwY31/R9bLe/e/QcPtx+1dx4/efqss/v8k8kKzWDIMpHpy5gaEFzB0HIr4DLXQGUs4CK+elfnL65BG56pj7bMYSzpVPGUM2odNen0qmgpMtLTeFz5fT8IA+L3/H7gk/BNDcLw8G0QzK8nZD7p7LuKZeC7gNyC/eO9xdnPL3uL08lu632UZKyQoCwT1JgRGeR2XFFtORMwb0eFgZyyKzqFkYOKSjDjanmiOe46JsFppt2nLF6yqx0VlcaUMnaVktqZ2czV5L9yo8Kmh+OKq7ywoFgzKC0EthmuPcIJ18CsKB2gTHN3VsxmVFNmnZPt7uqYKWQSrC7XryKoSgyjzu7VAguf7Q1P7OwIDwI/t2tKo9zZ08tdj25qyICr5n8GfDqzR4RwtaanQcENy6R006oopZKLMoGUFsLOq8ikv3GXuX3gFAvaGMkVPqfK4HPQPN2UMY4E81cm/iPTjuJMJLWb3Rr8x7dru8Ujm2t2FwwH/bBPztwCnqAmttFL9Aq9RgQdoGP0AZ2iIWLoK1qgb+i7t+MR78ALm9LW1m3PC7QW3skvm0cp1A==</latexit><latexit sha1_base64="VMddr955s5n6Rw6J+zJB2A1yElQ=">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</latexit><latexit sha1_base64="5jjUTIrSIWUa4bicGMZzldKJ1OQ=">AAADiHicvVJNb9NAEN3GfJSUjxSOXFZEkThEkTdgtT5UqoqQOBaV0EpxFK3X42TV9draHbdElv8Ev4Yr/Av+DeskQJJyZiRLz29m3uy+nbhQ0qLv/9xreffuP3i4/6h98PjJ02edw+efbV4aASORq9xcxdyCkhpGKFHBVWGAZ7GCy/j6XZO/vAFjZa4/4aKAScZnWqZScHTUtNOvoqXI2MziSeUP/CAMmN/3B4HPwjcNCMPjt0FQ30xZPe10XcUy6F3A1qBL1nE+PWy9j5JclBloFIpbO2bDAicVNyiFgrodlRYKLq75DMYOap6BnVTLE9W055iEprlxn0a6ZDc7Kp5Zu8hiV5lxnNvdXEP+KzcuMT2eVFIXJYIWq0FpqSjmtPGIJtKAQLVwgAsj3VmpmHPDBTon273NMTPIM0Cz2L6K4jqxgju7NwsQvuCtTHB+QoeBX+CW0rhw9vQL12NWNWwo9ep/DnI2xxPGpN7SM6DhVuRZ5qZVUcozqRYJpLxUWFeRTX/jnnD7IDlVfGWk1PSCa0svwMh0V8Y6EuxfmfiPTDuKc5U0bvYa8B/fru0Wj+2u2V0wGg7CAfvod0/P1hu4T16SV+Q1YeSInJIP5JyMiCBfyTfynfzwDjzmHXnhqrS1t+55QbbCO/sFVlAmJw==</latexit>

v2<latexit sha1_base64="4YIz4uCXPIJFh5N6VisrITWuWBQ=">AAADiHicvVJNa9tAEN1Y/UidfjjtsVCWBkMPxmjdikSHQEgp9JiQuglYxqxWI3vJaiV2R0mN8J/or8m1/Re99ad0ZaWt7fTcAcHTm5k3u28nLpS06Ps/tlrevfsPHm4/au88fvL0WWf3+Webl0bAUOQqNxcxt6CkhiFKVHBRGOBZrOA8vnxf58+vwFiZ6084L2Cc8amWqRQcHTXp9KpoKTIy03hc+X0/CAPm9/x+4LPwbQ3C8OBdECyuJoPFpLPnKpZB7wJ2C/aOXt2c/iSEnEx2Wx+iJBdlBhqF4taO2KDAccUNSqFg0Y5KCwUXl3wKIwc1z8COq+WJFrTrmISmuXGfRrpkVzsqnlk7z2JXmXGc2c1cTf4rNyoxPRhXUhclghbNoLRUFHNae0QTaUCgmjvAhZHurFTMuOECnZPt7uqYKeQZoJmvX0VxnVjBnd2rBQhf8FomODukg8AvcE1pVDh7eoXrMU0NG0jd/M9ATmd4yJjUa3oGNFyLPMvctCpKeSbVPIGUlwoXVWTT37gr3D5IThVvjJSannFt6RkYmW7KWEeC/SsT/5FpR3GuktrNbg3+49u13eKxzTW7C4aDfthnp24Bj0kT2+QleU3eEEb2yRH5SE7IkAjyldyQb+S7t+Mxb98Lm9LW1m3PC7IW3vEvuQoobw==</latexit><latexit sha1_base64="xIjw7/SK3hcuSsO/Bb4ervxBxJs=">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</latexit><latexit sha1_base64="xIjw7/SK3hcuSsO/Bb4ervxBxJs=">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</latexit><latexit sha1_base64="9bKAamGCKYEjX8tgGcthftCPHrU=">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</latexit>

v3<latexit sha1_base64="c6d7XuYaiZE3LC9TxHBjp9Z7zIg=">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</latexit><latexit sha1_base64="wSlFkhFotZPywZcmALLMy0vynHo=">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</latexit><latexit sha1_base64="wSlFkhFotZPywZcmALLMy0vynHo=">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</latexit><latexit sha1_base64="FuWsLx6+PgG2kXcYt6Xzx96Tp0w=">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</latexit>

v1, v2, v3 2 V ) u 2 V<latexit sha1_base64="2mozvWglVRno/VzyGj9ABZsM070=">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</latexit><latexit sha1_base64="IAN+3sTTtQTWmGKPTqWYPcp7qm4=">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</latexit><latexit sha1_base64="IAN+3sTTtQTWmGKPTqWYPcp7qm4=">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</latexit><latexit sha1_base64="3uUM+fo2qysYZk2oYCYGbo51qOs=">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</latexit>

V ✓ E0,<latexit sha1_base64="LFZY4QhUkGRVPdULCtihXgNka58=">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</latexit><latexit sha1_base64="yk68cJ/GKt/VEcb/kGY8r6bkgQA=">AAADbHicvVJRaxNBEN4m1dZobao+CEVYLJE+lHAXkNaHQlEKPlZq0kIuhrm9uWTp7t65O2cNR36Jr+p/8k/4G9zkqiapzw4cfPvNzDd7306cK+koCH6s1errd+5ubN5r3H+w9XC7ufOo57LCCuyKTGX2MgaHShrskiSFl7lF0LHCi/jqzSx/8Qmtk5l5T5McBxpGRqZSAHlq2NzuRa6IHRJ+5KcfgoNhcy9oB/Pgt0F4A/ZOnm59h/1X62fDndpplGSi0GhIKHCuH3ZyGpRgSQqF00ZUOMxBXMEI+x4a0OgG5fzmU97yTMLTzPrPEJ+zix0laOcmOvaVGmjsVnMz8l+5fkHp0aCUJi8IjagGpYXilPGZDTyRFgWpiQcgrPR35WIMFgR5sxqtxTEjzDSSnSz/igKTOAHe0cUCws90LRMaH/POyyCnJaV+7u05yH2PrWrCjjTVeYxyNKbjMJRmSc+iwWuRae2nlVEKWqpJgikUiqZl5NLfuCX8k0vgCiojpeHnYBw/RyvTVRnnSXR/ZeI/Mo0ozlQyc7M1A//x7Rp+8cLVNbsNep12GLTDd34DX7MqNtkue872WcgO2Ql7y85YlwlWsC/sK/tW+1l/Ut+tP6tKa2s3PY/ZUtRf/ALFeiC6</latexit><latexit sha1_base64="yk68cJ/GKt/VEcb/kGY8r6bkgQA=">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</latexit><latexit sha1_base64="3g5dqw5sFSVBZUTaHfD42zvSfKU=">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</latexit>

V ✓ E0,<latexit sha1_base64="LFZY4QhUkGRVPdULCtihXgNka58=">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</latexit><latexit sha1_base64="yk68cJ/GKt/VEcb/kGY8r6bkgQA=">AAADbHicvVJRaxNBEN4m1dZobao+CEVYLJE+lHAXkNaHQlEKPlZq0kIuhrm9uWTp7t65O2cNR36Jr+p/8k/4G9zkqiapzw4cfPvNzDd7306cK+koCH6s1errd+5ubN5r3H+w9XC7ufOo57LCCuyKTGX2MgaHShrskiSFl7lF0LHCi/jqzSx/8Qmtk5l5T5McBxpGRqZSAHlq2NzuRa6IHRJ+5KcfgoNhcy9oB/Pgt0F4A/ZOnm59h/1X62fDndpplGSi0GhIKHCuH3ZyGpRgSQqF00ZUOMxBXMEI+x4a0OgG5fzmU97yTMLTzPrPEJ+zix0laOcmOvaVGmjsVnMz8l+5fkHp0aCUJi8IjagGpYXilPGZDTyRFgWpiQcgrPR35WIMFgR5sxqtxTEjzDSSnSz/igKTOAHe0cUCws90LRMaH/POyyCnJaV+7u05yH2PrWrCjjTVeYxyNKbjMJRmSc+iwWuRae2nlVEKWqpJgikUiqZl5NLfuCX8k0vgCiojpeHnYBw/RyvTVRnnSXR/ZeI/Mo0ozlQyc7M1A//x7Rp+8cLVNbsNep12GLTDd34DX7MqNtkue872WcgO2Ql7y85YlwlWsC/sK/tW+1l/Ut+tP6tKa2s3PY/ZUtRf/ALFeiC6</latexit><latexit sha1_base64="yk68cJ/GKt/VEcb/kGY8r6bkgQA=">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</latexit><latexit sha1_base64="3g5dqw5sFSVBZUTaHfD42zvSfKU=">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</latexit>

Page 9: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Properties of Leavitt path algebras

prime downward directed

LK(E)<latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">AAADYHicvVJbaxNBFJ4mXtp4aaNv+jIYAhUkZIOiPhSKUhD0oVLTFrIhnJ09m512ZnaZOWsNS/6Dr/rPfPaPOJuNmqQ+e2Dgm+9c55sT5Uo66vd/bDWaN27eur2907pz99793b32g1OXFVbgUGQqs+cROFTS4JAkKTzPLYKOFJ5Fl28r/9lntE5m5hPNchxrmBqZSAHkqdMPk/f7R08ne51+r78wfh0ES9BhSzuetBtHYZyJQqMhocC5UTDIaVyCJSkUzlth4TAHcQlTHHloQKMbl4tx57zrmZgnmfXHEF+wqxklaOdmOvKRGih1m76K/JdvVFDyalxKkxeERtSNkkJxynj1dh5Li4LUzAMQVvpZuUjBgiCv0FqXKWYayc7mre5qAwUmdgK8jCsRIeEXupIxpQd88KKf03pO7uV5lvscW8cEA2nqe4pymtJBEEizVs+iwSuRae27lWECWqpZjAkUiuZl6JLfuCv8P0vgCmohpeEnYBw/QSuTzTLOk+j+lon+lGmFUabiSs1uBf7j37X84gWba3YdDAe9173g4/PO4ZvlBm6zx+wJ22cBe8kO2Tt2zIZMsAv2lX1j3xs/mzvN3Wa7Dm1sLXMesjVrPvoFfE0ahQ==</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit>

E<latexit sha1_base64="FKJjd8xw0DoagSjQqfenD04oLjA=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">AAADW3icvVLdahNBFJ5mq9a1aqt45c1gCHghYTdQtBfBohS8bKmxhWwoZ2fPJkNnZpeZs61hyRN4q0/gw/gI4o3P4iRbNUm99sDAN9/5ne9MWirpKIp+bLSCzVu372zdDe9t33/wcGf30QdXVFbgQBSqsGcpOFTS4IAkKTwrLYJOFZ6mF2/n/tNLtE4W5j1NSxxpGBuZSwHkqePD85121I0Wxm+C+Bq0X38L++XX7+HR+W7rMMkKUWk0JBQ4N4x7JY1qsCSFwlmYVA5LEBcwxqGHBjS6Ub2YdMY7nsl4Xlh/DPEFu5xRg3ZuqlMfqYEmbt03J//lG1aUvxrV0pQVoRFNo7xSnAo+fzbPpEVBauoBCCv9rFxMwIIgL85KlzEWGslOZ2FnuYECkzkBXsGliITwI13JjCZ93tuLSlrNKb08L0qfY5uYuCdNc5+gHE+oH8fSrNSzaPBKFFr7bnWSg5ZqmmEOlaJZnbj8N+4Iv2IJXEEjpDT8BIzjJ2hlvl7GeRLd3zLpnzJhkhYqm6vZmYP/uLvQf7x4/ZvdBINed78bH0ftgzessS32lD1jz1nMXrID9o4dsQETDNkn9pl9af0MNoMw2G5CWxvXOY/ZigVPfgEFYBxJ</latexit><latexit sha1_base64="M0ROzkQIVaOvJ4omKdKT8tj4tXc=">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</latexit>

v<latexit sha1_base64="S52Y8C68YUN59ZYa74Hw/bvPAhc=">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</latexit><latexit sha1_base64="Y/H/pdQD6mwWuQ4XMEcgIAcPm2A=">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</latexit><latexit sha1_base64="Y/H/pdQD6mwWuQ4XMEcgIAcPm2A=">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</latexit><latexit sha1_base64="k1d6eUwxFOvn4dWOMoY+dFgT+YM=">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</latexit>

u<latexit sha1_base64="kYiNsLEMnKqUGhzgoOzbf2u3p7w=">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</latexit><latexit sha1_base64="N6nLa5gxfeCi3/q3y3PikJdne+Q=">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</latexit><latexit sha1_base64="N6nLa5gxfeCi3/q3y3PikJdne+Q=">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</latexit><latexit sha1_base64="U2EiY8yt25I08kr2HkgfCIk4Eeg=">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</latexit>

w<latexit sha1_base64="dDx1g8htmTFqOBrduaBY+obLiEw=">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</latexit><latexit sha1_base64="jWESv8FHE++BSlam1or48Y4aZfs=">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</latexit><latexit sha1_base64="jWESv8FHE++BSlam1or48Y4aZfs=">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</latexit><latexit sha1_base64="Wgdq8P0Rl4xSCrZtj/R8d+v+u0c=">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</latexit>

Page 10: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Properties of Leavitt path algebras

one sided artinian acyclic, row-finite, infinite paths end in a sink

LK(E)<latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit>

E<latexit sha1_base64="FKJjd8xw0DoagSjQqfenD04oLjA=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">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</latexit><latexit sha1_base64="M0ROzkQIVaOvJ4omKdKT8tj4tXc=">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</latexit>

v1<latexit sha1_base64="8PAKmmixM9V7EuJjn4WJYmj2zAM=">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</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">AAADXXicvVLNbtNAEN4mUEoopT8HDlxWVJEQQpEdsGgOlSp+JI5FIbRSEkXj9ThZdXdt7Y5bIquPwBWegTfgMbhy41FYxxSSCq6MZOnzNzPf7H47ca6koyD4vtZo3ri5fmvjduvO5t2te9s7u+9dVliBA5GpzJ7G4FBJgwOSpPA0twg6VngSn72s8ifnaJ3MzDua5zjWMDUylQLIU/3zSTjZ3g86QdSLwoAHnSgIe08r0OsdPIsiHnaCRewf7X599W3vy+PjyU7j9SjJRKHRkFDg3DDs5jQuwZIUCi9bo8JhDuIMpjj00IBGNy4XZ73kbc8kPM2s/wzxBbvcUYJ2bq5jX6mBZu56riL/lhsWlB6MS2nygtCIelBaKE4Zry7OE2lRkJp7AMJKf1YuZmBBkLen1V4eM8VMI9n56lUUmMQJ8B4uFxB+oAuZ0OyQd6MgpxWlYe7teZL7HlvXhF1p6v8ZyumMDsNQmhU9iwYvRKa1n1aOUtBSzRNMoVB0WY5ceoXbwj+yBK6gNlIa3gfjeB+tTK/LOE+i+yMT/5ZpjeJMJZWb7Qr8x7dr+cW72i7+bzDodnqd4K1fwBesjg32gD1kj1jInrMj9oYdswETbMo+sk/sc+NHc7252dyqSxtrv3r22Eo07/8EwHUdLg==</latexit><latexit sha1_base64="BRBckf5J2itsIQ6MV2lt3OdGnRs=">AAADXXicvVLNbtNAEN4mUEoopT8HDlxWVJEQQpEdsGgOlSp+JI5FIbRSEkXj9ThZdXdt7Y5bIquPwBWegTfgMbhy41FYxxSSCq6MZOnzNzPf7H47ca6koyD4vtZo3ri5fmvjduvO5t2te9s7u+9dVliBA5GpzJ7G4FBJgwOSpPA0twg6VngSn72s8ifnaJ3MzDua5zjWMDUylQLIU/3zSTjZ3g86QdSLwoAHnSgIe08r0OsdPIsiHnaCRewf7X599W3vy+PjyU7j9SjJRKHRkFDg3DDs5jQuwZIUCi9bo8JhDuIMpjj00IBGNy4XZ73kbc8kPM2s/wzxBbvcUYJ2bq5jX6mBZu56riL/lhsWlB6MS2nygtCIelBaKE4Zry7OE2lRkJp7AMJKf1YuZmBBkLen1V4eM8VMI9n56lUUmMQJ8B4uFxB+oAuZ0OyQd6MgpxWlYe7teZL7HlvXhF1p6v8ZyumMDsNQmhU9iwYvRKa1n1aOUtBSzRNMoVB0WY5ceoXbwj+yBK6gNlIa3gfjeB+tTK/LOE+i+yMT/5ZpjeJMJZWb7Qr8x7dr+cW72i7+bzDodnqd4K1fwBesjg32gD1kj1jInrMj9oYdswETbMo+sk/sc+NHc7252dyqSxtrv3r22Eo07/8EwHUdLg==</latexit>

v2<latexit sha1_base64="RnLauIjsfIi1c/EKrcB2wuxx9a8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">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</latexit><latexit sha1_base64="vdaCPE1NSJIO2U3ieYpHDz91CA8=">AAADXXicvVLNbtNAEN4mUEoopT8HDlxWVJEQQpEdsGgOlSp+JI5FIbRSEkXj9ThZdXdt7Y5bIquPwBWegTfgMbhy41FYxxSSCq6MZOnzNzPf7H47ca6koyD4vtZo3ri5fmvjduvO5t2te9s7u+9dVliBA5GpzJ7G4FBJgwOSpPA0twg6VngSn72s8ifnaJ3MzDua5zjWMDUylQLIU/3zSXeyvR90gqgXhQEPOlEQ9p5WoNc7eBZFPOwEi9g/2v366tvel8fHk53G61GSiUKjIaHAuWHYzWlcgiUpFF62RoXDHMQZTHHooQGNblwuznrJ255JeJpZ/xniC3a5owTt3FzHvlIDzdz1XEX+LTcsKD0Yl9LkBaER9aC0UJwyXl2cJ9KiIDX3AISV/qxczMCCIG9Pq708ZoqZRrLz1asoMIkT4D1cLiD8QBcyodkh70ZBTitKw9zb8yT3PbauCbvS1P8zlNMZHYahNCt6Fg1eiExrP60cpaClmieYQqHoshy59Aq3hX9kCVxBbaQ0vA/G8T5amV6XcZ5E90cm/i3TGsWZSio32xX4j2/X8ot3tV3832DQ7fQ6wVu/gC9YHRvsAXvIHrGQPWdH7A07ZgMm2JR9ZJ/Y58aP5npzs7lVlzbWfvXssZVo3v8Jw2wdLw==</latexit>

v3<latexit sha1_base64="aCJXJ5RlxA9vJSXn+kHy1M4mML0=">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</latexit><latexit sha1_base64="7+An/e4ZjGTsSKaG/UAenbk8Nsc=">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</latexit><latexit sha1_base64="7+An/e4ZjGTsSKaG/UAenbk8Nsc=">AAADXXicvVLNbtNAEN4mUIop/T1w4LKiioQQiuwUi+ZQqeJH4lgUQivFUbRej51Vd9fW7rglsvIIXOEZeAMegys3HoV1TCGp4MpIlj5/M/PN7rcTF1JY9P3va632rdvrdzbuevc2729t7+zuvbd5aTgMeS5zcx4zC1JoGKJACeeFAaZiCWfxxcs6f3YJxopcv8NZAWPFMi1SwRk6anA5OZzsHPhdP+yHgU/9bugH/cMa9PtHz8KQBl1/EQcne19ffdv/8uR0stt6HSU5LxVo5JJZOwp6BY4rZlBwCXMvKi0UjF+wDEYOaqbAjqvFWee045iEprlxn0a6YJc7KqasnanYVSqGU3szV5N/y41KTI/GldBFiaB5MygtJcWc1heniTDAUc4cYNwId1bKp8wwjs4er7M8JoNcAZrZ6lUk04nlzHm4XIDwAa9EgtNj2gv9AleURoWz52nhekxTE/SEbv6nILIpHgeB0Ct6BjRc8VwpN62KUqaEnCWQslLivIpseo073D2yYFSyxkih6YBpSwdgRHpTxjoS7B+Z+LeMF8W5TGo3OzX4j2/nucW73i76bzDsdftd/61bwBekiQ3ykDwij0lAnpMT8oackiHhJCMfySfyufWjvd7ebG81pa21Xz37ZCXaD34CxmMdMA==</latexit>

v4<latexit sha1_base64="5o7IKDY9gLFdRStvBpyGFyzmiOI=">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</latexit><latexit sha1_base64="DY7vSTAraABkoaKhE1CBCXv4ZaE=">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</latexit><latexit sha1_base64="DY7vSTAraABkoaKhE1CBCXv4ZaE=">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</latexit>

e2<latexit sha1_base64="+qvft35mNCYBd7mHkko9V+wUF/c=">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</latexit><latexit sha1_base64="4TWgrdRvjtxoRH9cYpisFS/0ZOc=">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</latexit><latexit sha1_base64="4TWgrdRvjtxoRH9cYpisFS/0ZOc=">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</latexit>

e1<latexit sha1_base64="Gahtq2xaFc9C2zq3tCEmh3z/KjE=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">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</latexit><latexit sha1_base64="oYJZZuJpNLm6airNbuKnjEqZwV4=">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</latexit>

e3<latexit sha1_base64="u6aps99kjMZnFt6LACGZVHxr8GA=">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</latexit><latexit sha1_base64="ko+763tzlQVosGPwibi3OupeYmY=">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</latexit><latexit sha1_base64="ko+763tzlQVosGPwibi3OupeYmY=">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</latexit> v 2 E0 ) |s�1(v)| < 1

<latexit sha1_base64="WyIKkiyRr/NQPEC0WbKRLdfWuS8=">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</latexit><latexit sha1_base64="WyIKkiyRr/NQPEC0WbKRLdfWuS8=">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</latexit><latexit sha1_base64="WyIKkiyRr/NQPEC0WbKRLdfWuS8=">AAADg3icvVLNbhMxEHazFEr4S8uRi0UUVAREu1ERPRCpAlXiWChpK2XTyOudTaza3pU9m7Da5g14Gq7wIrwN3iRAknJmJEuf5+cb+5uJMiks+v7PrZp3a/v2nZ279Xv3Hzx81NjdO7Npbjj0eCpTcxExC1Jo6KFACReZAaYiCefR1fsqfj4BY0WqP2ORwUCxkRaJ4Ayda9h4NgmFpseXfvhJjMbIjEmn9Npelq+C2f7k+fVbF06wGDaaftufG70JgiVokqWdDHdrx2Gc8lyBRi6Ztf2gk+GgZAYFlzCrh7mFjPErNoK+g5opsINy/qEZbTlPTJPUuKORzr2rFSVT1hYqcpmK4dhuxirnv2L9HJPDQSl0liNovmiU5JJiSit1aCwMcJSFA4wb4d5K+ZgZxtFpWG+tthlBqgBNsf4VyXRsOXNCryYgfMGpiHHcpZ3XfoZrTP3MyfMyczVmkRN0hF7cx1ANpRsEQq/xGdAw5alSrlsZJkwJWcSQsFzirAxt8hu3uNsEwahkCyHdqE+ZtvQUjEg2aaxzgv1LE/2hqYdRKuNKzVYF/uPs6m7xgs01uwnOOu3AbwcfD5pH75YruEOekKdknwTkDTkiH8gJ6RFOvpJv5Dv54W17L7yOd7BIrW0tax6TNfO6vwCYGCeA</latexit><latexit sha1_base64="WyIKkiyRr/NQPEC0WbKRLdfWuS8=">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</latexit>

Page 11: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Properties of Leavitt path algebras

one sided notherian cycles has no exits, row-finite, infinite paths end in a sink or in a cycle

LK(E)<latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit><latexit sha1_base64="vblG++LoX+MBfPnUsMY8o57cJkY=">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</latexit>

E<latexit sha1_base64="FKJjd8xw0DoagSjQqfenD04oLjA=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">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</latexit><latexit sha1_base64="b2agCkUlMb7l2aswhuwEojuPiLc=">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</latexit><latexit sha1_base64="M0ROzkQIVaOvJ4omKdKT8tj4tXc=">AAADW3icvVLPaxNBFJ5mq9a1aqt48jIYAh4k7AaK9lAoSsFjS40tZEN5O/s2O3Rmdpl52xqW/AVe9Y/z4t/iJBs1ST37YOCb7/2cb15aKekoin5sdYLte/cf7DwMH+0+fvJ0b//ZZ1fWVuBQlKq0lyk4VNLgkCQpvKwsgk4VXqTXH+b+ixu0TpbmE00rHGuYGJlLAeSps5OrvW7UjxbG74J4CbpsaadX+52TJCtFrdGQUODcKB5UNG7AkhQKZ2FSO6xAXMMERx4a0OjGzWLSGe95JuN5af0xxBfsakYD2rmpTn2kBircpm9O/ss3qil/N26kqWpCI9pGea04lXz+bJ5Ji4LU1AMQVvpZuSjAgiAvzlqXCZYayU5nYW+1gQKTOQFewZWIhPAL3cqMiiM+OIgqWs+pvDxvKp9j25h4IE17L1BOCjqKY2nW6lk0eCtKrX23JslBSzXNMIda0axJXP4b94T/YglcQSukNPwcjOPnaGW+WcZ5Et3fMumfMmGSliqbq9mbg//4d6FfvHhzze6C4aB/2I/Pou7x++UG7rCX7BV7zWL2lh2zj+yUDZlgyL6yb+x752ewHYTBbhva2VrmPGdrFrz4Be0MGQg=</latexit>

Page 12: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Ring theoretic properties of Leavitt path algebras

[Ara, Goodearl ’12] Leavitt path algebras are hereditary.

[Abrams, Ara, Siles Molina ’17] Leavitt path algebras are semiprimitive.

Leavitt path algebras are isomorphic to their opposite.

Page 13: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

A ring R is Bézout in case every finitely generated one-sided ideal is principal.

Bézout rings

The Bézout property need not pass to (full) corners. In particular it is not a Morita invariant.

Warfield showed that if is Bézout, then so is Mn(R)<latexit sha1_base64="qO6mYo6ZL8Q0242kqRf0+J1t814=">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</latexit><latexit sha1_base64="KGCBVnWqfkX9QpVx41gI9P3e5LM=">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</latexit><latexit sha1_base64="KGCBVnWqfkX9QpVx41gI9P3e5LM=">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</latexit><latexit sha1_base64="rrYFddCwhKY3ZtCvYu0xM0XNj6M=">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</latexit>

R<latexit sha1_base64="p6JjiDfjiiiXYmw0ahdIxPnpxiE=">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</latexit><latexit sha1_base64="8JwLG+xyD3AKhlbXbi3uB/RyfrU=">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</latexit><latexit sha1_base64="8JwLG+xyD3AKhlbXbi3uB/RyfrU=">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</latexit><latexit sha1_base64="pdl8H/AfD0WZ40wQnX9xdJIDKQs=">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</latexit>

Intuitively, the Bézout property allows us to do some “Number Theory”, since for each , there exists for which .

a, b 2 R<latexit sha1_base64="vhfpOhjLGg+ZDx/mLwRW4YUaXOE=">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</latexit><latexit sha1_base64="X+W9PbvGbNwIF3AU/uBcnnfD2FI=">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</latexit><latexit sha1_base64="X+W9PbvGbNwIF3AU/uBcnnfD2FI=">AAADYnicvVLNbhMxEHYTfkoKtIEjFbKoInGoomwkBD1UqoQqcSyU0EjZqJr1zmat2t6VPdsSrfIKHLjCe3DkOXgADrwF3mwKScqZkSx9/ubP/maiXElHvd6PjUbz1u07dzfvtbbuP3i4vdN+9MFlhRU4EJnK7DACh0oaHJAkhcPcIuhI4Vl08bryn12idTIz72ma41jDxMhECiBPDWE/CqXh78539nrd3tz4TRAswN7R7vavb9+ffjo5bzeOwzgThUZDQoFzo6Cf07gES1IonLXCwmEO4gImOPLQgEY3LucPnvGOZ2KeZNYfQ3zOLmeUoJ2b6shHaqDUrfsq8l++UUHJq3EpTV4QGlE3SgrFKePV73ksLQpSUw9AWOnfykUKFgR5jVa6TDDTSHY6a3WWGygwsRPghVyKCAk/0pWMKT3k/Re9nFZzci/Pfu5zbB0T9KWp7ynKSUqHQSDNSj2LBq9EprXvVoYJaKmmMSZQKJqVoUuucUf4SUvgCmoh/ShPwTh+ilYm62WcJ9H9LRP9KdMKo0zFlZqdCvzH2bX84gXra3YTDPrdg27w1i/gMattkz1hz9hzFrCX7Ii9YSdswART7DP7wr42fja3mu3m4zq0sbHIWdyvrbn7G4dNHxY=</latexit><latexit sha1_base64="DuW5HYTC3CbkEgzEvm/UVlxo1wY=">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</latexit>

c 2 R<latexit sha1_base64="3AdXFQsH95Px8Qq7W6R0Ak/RxLw=">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</latexit><latexit sha1_base64="nZjkO9K+8DJ4YFQj4a74E6pcGTI=">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</latexit><latexit sha1_base64="nZjkO9K+8DJ4YFQj4a74E6pcGTI=">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</latexit><latexit sha1_base64="yKM2KWkZBDvqWo9esEd0nuO09b8=">AAADYHicvVJLbxMxEHazPNrwaAM3uFhEkTigaDcSAg6VKqFKHAslbaVsVM16ZxNTP1b2LCVa5T9whX/GmT+CNwmQpJwZydLnb172N5OVSnqK4x87rejW7Tt3d/fa9+4/eLh/0Hl05m3lBA6FVdZdZOBRSYNDkqTwonQIOlN4nl29bfznn9F5ac1HmpU41jAxspACKFBnIpWGf7g86Mb9eGH8JkhWoMtWdnLZaR2nuRWVRkNCgfejZFDSuAZHUiict9PKYwniCiY4CtCARj+uF8+d815gcl5YF44hvmDXM2rQ3s90FiI10NRv+xryX75RRcXrcS1NWREasWxUVIqT5c3feS4dClKzAEA4Gd7KxRQcCAoKbXSZoNVIbjZv99YbKDC5FxBkXItICb/QtcxpesgHL+OSNnPKIM+LMuS4ZUwykGZ5n6KcTOkwSaTZqOfQ4LWwWodudVqAlmqWYwGVonmd+uI37okwZwlcwVLIMMpTMJ6fopPFdhkfSPR/y2R/yrTTzKq8UbPXgP84u3ZYvGR7zW6C4aD/pp+8j7tHx6sN3GVP2TP2nCXsFTti79gJGzLBPrGv7Bv73voZ7UX7UWcZ2tpZ5TxmGxY9+QXszxsA</latexit>

Ra + Rb = Rc<latexit sha1_base64="bv5rNADRt8IfnXQhp36lOizclRI=">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</latexit><latexit sha1_base64="asPdubXEh47+5HBrdtQcMY6Z7+g=">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</latexit><latexit sha1_base64="asPdubXEh47+5HBrdtQcMY6Z7+g=">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</latexit><latexit sha1_base64="uH977PBLDW2KllmX1VkrqB/3pLo=">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</latexit>

Page 14: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Mn(K)<latexit sha1_base64="YZhnAIybw35uFRHvDK/QMaXJz2k=">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</latexit><latexit sha1_base64="YZhnAIybw35uFRHvDK/QMaXJz2k=">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</latexit><latexit sha1_base64="YZhnAIybw35uFRHvDK/QMaXJz2k=">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</latexit><latexit sha1_base64="YZhnAIybw35uFRHvDK/QMaXJz2k=">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</latexit>

K[x, x�1]<latexit sha1_base64="hCHYNinRkK5Pkl6URTwIZFi7Gj4=">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</latexit><latexit sha1_base64="hCHYNinRkK5Pkl6URTwIZFi7Gj4=">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</latexit><latexit sha1_base64="hCHYNinRkK5Pkl6URTwIZFi7Gj4=">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</latexit><latexit sha1_base64="hCHYNinRkK5Pkl6URTwIZFi7Gj4=">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</latexit>

LK(1, n)<latexit sha1_base64="foWPRLayAPGV8TmVp66dQ6mYuDI=">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</latexit><latexit sha1_base64="foWPRLayAPGV8TmVp66dQ6mYuDI=">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</latexit><latexit sha1_base64="foWPRLayAPGV8TmVp66dQ6mYuDI=">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</latexit><latexit sha1_base64="foWPRLayAPGV8TmVp66dQ6mYuDI=">AAADYnicvVJbaxNBFJ4mXmrqpbGP+jAYAhVK2A2I7UOhKIKgD5UaG8iGcHb2bHbozOwyc9a6LPkTvuof8wf4P5xc1CT12QMD33znOt+cuFDSURD82Gk0b92+c3f3Xmvv/oOHj/bbjz+5vLQCByJXuR3G4FBJgwOSpHBYWAQdK7yMr17P/Zef0TqZm49UFTjWMDUylQLIU8P3k3eH4ZF5PtnvBL1gYfwmCFegw1Z2Pmk33kRJLkqNhoQC50Zhv6BxDZakUDhrRaXDAsQVTHHkoQGNblwvBp7xrmcSnubWH0N8wa5n1KCdq3TsIzVQ5rZ9c/JfvlFJ6fG4lqYoCY1YNkpLxSnn89fzRFoUpCoPQFjpZ+UiAwuCvEYbXaaYayRbzVrd9QYKTOIEeCHXIiLCL3QtE8pOef9FUNBmTuHlOSp8jl3GhH1plvcM5TSj0zCUZqOeRYPXItfad6ujFLRUVYIplIpmdeTS37gr/E9L4AqWQkrDL8A4foFWpttlnCfR/S0T/ynTiuJcJXM1u3PwH/+u5Rcv3F6zm2DQ7530wg9B5+zVagN32RP2jB2ykL1kZ+wtO2cDJphiX9k39r3xs7nXbDcPlqGNnVXOAduw5tNfWIkbGw==</latexit>

⇠= LK(1, n)n<latexit sha1_base64="4Yp6+FBStOJ6frRdpHzf/K4KPUA=">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</latexit><latexit sha1_base64="4Yp6+FBStOJ6frRdpHzf/K4KPUA=">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</latexit><latexit sha1_base64="4Yp6+FBStOJ6frRdpHzf/K4KPUA=">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</latexit><latexit sha1_base64="4Yp6+FBStOJ6frRdpHzf/K4KPUA=">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</latexit>

KhX,Y |XY = 1i<latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="X+n3Rp8U7Dfa3Z8kZ0AhjfisSqg=">AAADTHicvVJbi9NAFJ5tvdS46u6zL4NLwQcpSUHUhwVBBB9X1roLTVlOJifNsHMJMyeuIfQP+OqvE/wxTpqqbddnDwx8853rfHOySklPcfzjYDC8c/fe/dGD6OFh9Ojxk6PDz97WTuBMWGXdZQYelTQ4I0kKLyuHoDOFF9n1u85/8QWdl9Z8oqbChYalkYUUQIE6uzo6iSfx2vhtkGzACdvY1fHgfZpbUWs0JBR4P0+mFS1acCSFwlWU1h4rENewxHmABjT6Rbuec8XHgcl5YV04hvia3c5oQXvf6CxEaqDS7/s68l++eU3F60UrTVUTGtE3KmrFyfLu0TyXDgWpJgAQToZZuSjBgaAgzU6XJVqN5JpVNN5uoMDkXkDQbysiJfxKNzKn8pRPX8YV7eZUQZ4XVchxfUwylaa/lyiXJZ0miTQ79RwavBFW69CtTQvQUjU5FlArWrWpL37jsQgfLIEr6IWUhp+D8fwcnSz2y/hAov9bJvtTJkozq/JOzXEH/uPfRWHvkv0tuw1m08mbSfIxZiP2lD1jz1nCXrG37AM7YzMmWM6+se+Dn8PBcNSv5+Bgs6fHbMeG0S9/uRcG</latexit><latexit sha1_base64="5u8cwuk5oBD+45TWqvxqJF7dwGw=">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</latexit><latexit sha1_base64="5u8cwuk5oBD+45TWqvxqJF7dwGw=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">AAADdHicvVJLixNBEO7N+FjjK6sXQYTGEPCwhJmAqIfAogiCl5U1bpZMCDU9NUmz3T1Dd43rMMZf41X/j7/Eq52HmmQ9W9Dw1Vev7q8rKZR0FIY/9hrBlavXru/faN68dfvO3dbBvQ8uL63AgchVbocJOFTS4IAkKRwWFkEnCk+T81eL+OlHtE7m5j1VBY41TI3MpADy1KT14G2swEwV8uHh2efhWT+K7dKftNphN1wavwyiNWiztR1PDhqv4zQXpUZDQoFzo6hX0LgGS1IonDfj0mEB4hymOPLQgEY3rpdPmPOOZ1Ke5dYfQ3zJblbUoJ2rdOIzNdDM7cYW5L9io5Ky5+NamqIkNGI1KCsVp5wv9OCptChIVR6AsNLflYsZWBDkVduaMsVcI9lq3uxsDvDypU6Al3YjIyb8RBcypVmf956GBW3XFF6ew8LX2FVO1JNm5c9QTmfUjyJptvpZNHghcq39tDrOQEtVpZhBqWhexy77jTvC/70ErmAlpDT8BIzjJ2hlttvGeRLd3zbJnzbNOMlVulCzswD/8e+afvGi3TW7DAa97otu9C5sH71cb+A+e8gesycsYs/YEXvDjtmACfaFfWXf2PfGz+BR0A46q9TG3rrmPtuyoPsL5JAiYQ==</latexit><latexit sha1_base64="zZBmgxqdhmWywJj/27rRPXBvlxU=">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</latexit>

and are Bézout

and hence it is Bézout

is Bézout [Gerritzen, ’00]

Bézout rings and Leavitt path algebras

FMN(K)<latexit sha1_base64="mA9TdQ9YKCZXgH3oBdfQpXEcigQ=">AAADbXicvVLbihNBEO1NvKzxlij4okhjCK6whExQ1IeFRVEEUVbWuAuZEGp6apJmu3uG7hrjMORTfNVv8i/8BHuSqEnWZwsaTp+6cqqiTElHvd6PnVr9wsVLl3evNK5eu37jZrN165NLcytwIFKV2tMIHCppcECSFJ5mFkFHCk+is5eV/+QzWidT85GKDEcaJkYmUgB5atxsvX43LkMNNI0i/n6+9/bRuNnudXsL4+dBsAJttrKjcav2KoxTkWs0JBQ4Nwz6GY1KsCSFwnkjzB1mIM5ggkMPDWh0o3Ix+5x3PBPzJLX+GeILdj2jBO1coSMfWU3ptn0V+S/fMKfk2aiUJssJjVg2SnLFKeWVEDyWFgWpwgMQVvpZuZiCBUFero0uE0w1ki3mjc56AwUmdgK8pmsRIeEXmsmYpge8/6SX0WZO5uXZz3yOXcYEfWmW/ynKyZQOgkCajXoWDc5EqrXvVoYJaKmKGBPIFc3L0CW/cUf4pUvgCpZCSsOPwTh+jFYm22WcJ9H9LRP9KdMIo1TFlZqdCvzH3TX84QXbZ3YeDPrd593gw+P24YvVBe6yu+wB22MBe8oO2Rt2xAZMsBn7yr6x77Wf9Tv1e/X7y9DazirnNtuw+sNfZcwfVg==</latexit><latexit sha1_base64="mA9TdQ9YKCZXgH3oBdfQpXEcigQ=">AAADbXicvVLbihNBEO1NvKzxlij4okhjCK6whExQ1IeFRVEEUVbWuAuZEGp6apJmu3uG7hrjMORTfNVv8i/8BHuSqEnWZwsaTp+6cqqiTElHvd6PnVr9wsVLl3evNK5eu37jZrN165NLcytwIFKV2tMIHCppcECSFJ5mFkFHCk+is5eV/+QzWidT85GKDEcaJkYmUgB5atxsvX43LkMNNI0i/n6+9/bRuNnudXsL4+dBsAJttrKjcav2KoxTkWs0JBQ4Nwz6GY1KsCSFwnkjzB1mIM5ggkMPDWh0o3Ix+5x3PBPzJLX+GeILdj2jBO1coSMfWU3ptn0V+S/fMKfk2aiUJssJjVg2SnLFKeWVEDyWFgWpwgMQVvpZuZiCBUFero0uE0w1ki3mjc56AwUmdgK8pmsRIeEXmsmYpge8/6SX0WZO5uXZz3yOXcYEfWmW/ynKyZQOgkCajXoWDc5EqrXvVoYJaKmKGBPIFc3L0CW/cUf4pUvgCpZCSsOPwTh+jFYm22WcJ9H9LRP9KdMIo1TFlZqdCvzH3TX84QXbZ3YeDPrd593gw+P24YvVBe6yu+wB22MBe8oO2Rt2xAZMsBn7yr6x77Wf9Tv1e/X7y9DazirnNtuw+sNfZcwfVg==</latexit><latexit sha1_base64="mA9TdQ9YKCZXgH3oBdfQpXEcigQ=">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</latexit><latexit sha1_base64="mA9TdQ9YKCZXgH3oBdfQpXEcigQ=">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</latexit>

,

[Abrams, Mantese, - ’18]Leavitt path algebras are Bézout.

Page 15: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Theorem [Hazrat, Rangaswamy ’16]. Any Leavitt path algebra is the direct limit of unital subalgebras, each one isomorphic to the Leavitt path algebra of a finite graph.

Proof: main ingredients

1) Reduction to unital Leavitt path algebras:

2) Reduction to Leavitt path algebras associated to graphs containing source vertices or source cycles:

Theorem [Abrams, Nam, Phus ’15]. The Leavitt path algebra associated to a finite graph which contains neither source vertices nor source cycles is Bézout.

Page 16: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Proof: main ingredients3) Induction on the number of vertices:

KhX,Y |XY = 1i<latexit sha1_base64="q/vzHXuI2tXLRVTznUbFqbVG/OM=">AAACAHicbVBNS8NAEN34WetX1YvgZbEIHqQkXqwHoeBF8FLB2JQmlM122i7dbMLuRiixXvwrXjyoePVnePPfuE170NYHA2/fm2FnXphwprRtf1sLi0vLK6uFteL6xubWdmln907FqaTg0pjH0guJAs4EuJppDl4igUQhh0Y4uBz7jXuQisXiVg8TCCLSE6zLKNFGapf2r31ORI8D9k6aD17zwvFl/m6XynbFzoHniTMlZTRFvV368jsxTSMQmnKiVMuxEx1kRGpGOYyKfqogIXRAetAyVJAIVJDlF4zwkVE6uBtLU0LjXP09kZFIqWEUms6I6L6a9cbif14r1d1qkDGRpBoEnXzUTTnWMR7HgTtMAtV8aAihkpldMe0TSag2oRVNCM7syfPEPa2cV5wbu1yrTtMooAN0iI6Rg85QDV2hOnIRRY/oGb2iN+vJerHerY9J64I1ndlDf2B9/gCrpZXo</latexit><latexit sha1_base64="q/vzHXuI2tXLRVTznUbFqbVG/OM=">AAACAHicbVBNS8NAEN34WetX1YvgZbEIHqQkXqwHoeBF8FLB2JQmlM122i7dbMLuRiixXvwrXjyoePVnePPfuE170NYHA2/fm2FnXphwprRtf1sLi0vLK6uFteL6xubWdmln907FqaTg0pjH0guJAs4EuJppDl4igUQhh0Y4uBz7jXuQisXiVg8TCCLSE6zLKNFGapf2r31ORI8D9k6aD17zwvFl/m6XynbFzoHniTMlZTRFvV368jsxTSMQmnKiVMuxEx1kRGpGOYyKfqogIXRAetAyVJAIVJDlF4zwkVE6uBtLU0LjXP09kZFIqWEUms6I6L6a9cbif14r1d1qkDGRpBoEnXzUTTnWMR7HgTtMAtV8aAihkpldMe0TSag2oRVNCM7syfPEPa2cV5wbu1yrTtMooAN0iI6Rg85QDV2hOnIRRY/oGb2iN+vJerHerY9J64I1ndlDf2B9/gCrpZXo</latexit><latexit sha1_base64="q/vzHXuI2tXLRVTznUbFqbVG/OM=">AAACAHicbVBNS8NAEN34WetX1YvgZbEIHqQkXqwHoeBF8FLB2JQmlM122i7dbMLuRiixXvwrXjyoePVnePPfuE170NYHA2/fm2FnXphwprRtf1sLi0vLK6uFteL6xubWdmln907FqaTg0pjH0guJAs4EuJppDl4igUQhh0Y4uBz7jXuQisXiVg8TCCLSE6zLKNFGapf2r31ORI8D9k6aD17zwvFl/m6XynbFzoHniTMlZTRFvV368jsxTSMQmnKiVMuxEx1kRGpGOYyKfqogIXRAetAyVJAIVJDlF4zwkVE6uBtLU0LjXP09kZFIqWEUms6I6L6a9cbif14r1d1qkDGRpBoEnXzUTTnWMR7HgTtMAtV8aAihkpldMe0TSag2oRVNCM7syfPEPa2cV5wbu1yrTtMooAN0iI6Rg85QDV2hOnIRRY/oGb2iN+vJerHerY9J64I1ndlDf2B9/gCrpZXo</latexit><latexit sha1_base64="q/vzHXuI2tXLRVTznUbFqbVG/OM=">AAACAHicbVBNS8NAEN34WetX1YvgZbEIHqQkXqwHoeBF8FLB2JQmlM122i7dbMLuRiixXvwrXjyoePVnePPfuE170NYHA2/fm2FnXphwprRtf1sLi0vLK6uFteL6xubWdmln907FqaTg0pjH0guJAs4EuJppDl4igUQhh0Y4uBz7jXuQisXiVg8TCCLSE6zLKNFGapf2r31ORI8D9k6aD17zwvFl/m6XynbFzoHniTMlZTRFvV368jsxTSMQmnKiVMuxEx1kRGpGOYyKfqogIXRAetAyVJAIVJDlF4zwkVE6uBtLU0LjXP09kZFIqWEUms6I6L6a9cbif14r1d1qkDGRpBoEnXzUTTnWMR7HgTtMAtV8aAihkpldMe0TSag2oRVNCM7syfPEPa2cV5wbu1yrTtMooAN0iI6Rg85QDV2hOnIRRY/oGb2iN+vJerHerY9J64I1ndlDf2B9/gCrpZXo</latexit>

⇠=<latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit>

⇠=<latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit>

⇠=<latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit>

⇠=<latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit>

⇠=<latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit>

M2(K)<latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit><latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit><latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit><latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit>

⇠=<latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit>

M2(K)<latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit><latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit><latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit><latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit>

M2(K)<latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit><latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit><latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit><latexit sha1_base64="xaCP8mNJZqHQoh827+8r+kUqeuc=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRahXsquF+ut4EUQoYLbFtqlZNNsG5tNliQrlKX/wYsHFa/+IG/+G9N2D9r6YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo5aWqSLUJ5JL1QmxppwJ6htmOO0kiuI45LQdjq9nfvuJKs2keDCThAYxHgoWMYKNlVp3/Yvq7Xm/XHFr7hxolXg5qUCOZr/81RtIksZUGMKx1l3PTUyQYWUY4XRa6qWaJpiM8ZB2LRU4pjrI5tdO0ZlVBiiSypYwaK7+nshwrPUkDm1njM1IL3sz8T+vm5qoHmRMJKmhgiwWRSlHRqLZ62jAFCWGTyzBRDF7KyIjrDAxNqCSDcFbfnmV+Be1q5p371Ya9TyNIpzAKVTBg0towA00wQcCj/AMr/DmSOfFeXc+Fq0FJ585hj9wPn8AkzKN9g==</latexit>

⇠=<latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit>

⇠=<latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit>

K<latexit sha1_base64="+k7vdyiaXvTSeWdlB7nWVXWB4M8=">AAAB53icbZA9SwNBEIbn4leMX1FLm8MgWIU7G7UyIKJgk4BnAskR9jZzyZq9vWN3TwhHfoGNhYqt/8Ta0s7Sf+Lmo9DEFxYe3neGnZkg4Uxpx/mycguLS8sr+dXC2vrG5lZxe+dWxamk6NGYx7IREIWcCfQ00xwbiUQSBRzrQf98lNfvUSoWixs9SNCPSFewkFGijVW7bhdLTtkZy54Hdwqls4/vy3cAqLaLn61OTNMIhaacKNV0nUT7GZGaUY7DQitVmBDaJ11sGhQkQuVn40GH9oFxOnYYS/OEtsfu746MREoNosBURkT31Gw2Mv/LmqkOT/yMiSTVKOjkozDlto7t0dZ2h0mkmg8MECqZmdWmPSIJ1eY2BXMEd3blefCOyqdlt+aUKhcwUR72YB8OwYVjqMAVVMEDCggP8ATP1p31aL1Yr5PSnDXt2YU/st5+AAbFj5M=</latexit><latexit sha1_base64="9iKOadZRBrr6lBxD+k88A0TZqfM=">AAAB53icbZC7SgNBFIbPxluMt3jpbAaDYBV2bdTKgIiCTQKuCSRLmJ2cTUZnL8zMCjHkCWwsVGx9AR/E0s4yb+LkUmjiDwMf/38Oc87xE8GVtu1vKzM3v7C4lF3OrayurW/kN7duVJxKhi6LRSxrPlUoeISu5lpgLZFIQ19g1b87G+bVe5SKx9G17ibohbQd8YAzqo1VuWrmC3bRHonMgjOBwunn4OJj52FQbua/Gq2YpSFGmgmqVN2xE+31qNScCeznGqnChLI72sa6wYiGqLzeaNA+2TdOiwSxNC/SZOT+7ujRUKlu6JvKkOqOms6G5n9ZPdXBsdfjUZJqjNj4oyAVRMdkuDVpcYlMi64ByiQ3sxLWoZIybW6TM0dwpleeBfeweFJ0KnahdA5jZWEX9uAAHDiCElxCGVxggPAIz/Bi3VpP1qv1Ni7NWJOebfgj6/0H1sSQ8A==</latexit><latexit sha1_base64="9iKOadZRBrr6lBxD+k88A0TZqfM=">AAAB53icbZC7SgNBFIbPxluMt3jpbAaDYBV2bdTKgIiCTQKuCSRLmJ2cTUZnL8zMCjHkCWwsVGx9AR/E0s4yb+LkUmjiDwMf/38Oc87xE8GVtu1vKzM3v7C4lF3OrayurW/kN7duVJxKhi6LRSxrPlUoeISu5lpgLZFIQ19g1b87G+bVe5SKx9G17ibohbQd8YAzqo1VuWrmC3bRHonMgjOBwunn4OJj52FQbua/Gq2YpSFGmgmqVN2xE+31qNScCeznGqnChLI72sa6wYiGqLzeaNA+2TdOiwSxNC/SZOT+7ujRUKlu6JvKkOqOms6G5n9ZPdXBsdfjUZJqjNj4oyAVRMdkuDVpcYlMi64ByiQ3sxLWoZIybW6TM0dwpleeBfeweFJ0KnahdA5jZWEX9uAAHDiCElxCGVxggPAIz/Bi3VpP1qv1Ni7NWJOebfgj6/0H1sSQ8A==</latexit><latexit sha1_base64="iJYvevAKnnZQIj8vcz4UXcngUcs=">AAAB53icbVBNS8NAEJ34WetX1aOXxSJ4KokX9VYQQfDSgrGFNpTNdtKu3WzC7kYoob/AiwcVr/4lb/4bt20O2vpg4PHeDDPzwlRwbVz321lZXVvf2Cxtlbd3dvf2KweHDzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH11O/9YRK80Tem3GKQUwHkkecUWOl5l2vUnVr7gxkmXgFqUKBRq/y1e0nLItRGiao1h3PTU2QU2U4EzgpdzONKWUjOsCOpZLGqIN8duiEnFqlT6JE2ZKGzNTfEzmNtR7Hoe2MqRnqRW8q/ud1MhNdBjmXaWZQsvmiKBPEJGT6NelzhcyIsSWUKW5vJWxIFWXGZlO2IXiLLy8T/7x2VfOabrV+U6RRgmM4gTPw4ALqcAsN8IEBwjO8wpvz6Lw4787HvHXFKWaO4A+czx8QP4yi</latexit>

⇠=<latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit> K<latexit sha1_base64="+k7vdyiaXvTSeWdlB7nWVXWB4M8=">AAAB53icbZA9SwNBEIbn4leMX1FLm8MgWIU7G7UyIKJgk4BnAskR9jZzyZq9vWN3TwhHfoGNhYqt/8Ta0s7Sf+Lmo9DEFxYe3neGnZkg4Uxpx/mycguLS8sr+dXC2vrG5lZxe+dWxamk6NGYx7IREIWcCfQ00xwbiUQSBRzrQf98lNfvUSoWixs9SNCPSFewkFGijVW7bhdLTtkZy54Hdwqls4/vy3cAqLaLn61OTNMIhaacKNV0nUT7GZGaUY7DQitVmBDaJ11sGhQkQuVn40GH9oFxOnYYS/OEtsfu746MREoNosBURkT31Gw2Mv/LmqkOT/yMiSTVKOjkozDlto7t0dZ2h0mkmg8MECqZmdWmPSIJ1eY2BXMEd3blefCOyqdlt+aUKhcwUR72YB8OwYVjqMAVVMEDCggP8ATP1p31aL1Yr5PSnDXt2YU/st5+AAbFj5M=</latexit><latexit sha1_base64="9iKOadZRBrr6lBxD+k88A0TZqfM=">AAAB53icbZC7SgNBFIbPxluMt3jpbAaDYBV2bdTKgIiCTQKuCSRLmJ2cTUZnL8zMCjHkCWwsVGx9AR/E0s4yb+LkUmjiDwMf/38Oc87xE8GVtu1vKzM3v7C4lF3OrayurW/kN7duVJxKhi6LRSxrPlUoeISu5lpgLZFIQ19g1b87G+bVe5SKx9G17ibohbQd8YAzqo1VuWrmC3bRHonMgjOBwunn4OJj52FQbua/Gq2YpSFGmgmqVN2xE+31qNScCeznGqnChLI72sa6wYiGqLzeaNA+2TdOiwSxNC/SZOT+7ujRUKlu6JvKkOqOms6G5n9ZPdXBsdfjUZJqjNj4oyAVRMdkuDVpcYlMi64ByiQ3sxLWoZIybW6TM0dwpleeBfeweFJ0KnahdA5jZWEX9uAAHDiCElxCGVxggPAIz/Bi3VpP1qv1Ni7NWJOebfgj6/0H1sSQ8A==</latexit><latexit sha1_base64="9iKOadZRBrr6lBxD+k88A0TZqfM=">AAAB53icbZC7SgNBFIbPxluMt3jpbAaDYBV2bdTKgIiCTQKuCSRLmJ2cTUZnL8zMCjHkCWwsVGx9AR/E0s4yb+LkUmjiDwMf/38Oc87xE8GVtu1vKzM3v7C4lF3OrayurW/kN7duVJxKhi6LRSxrPlUoeISu5lpgLZFIQ19g1b87G+bVe5SKx9G17ibohbQd8YAzqo1VuWrmC3bRHonMgjOBwunn4OJj52FQbua/Gq2YpSFGmgmqVN2xE+31qNScCeznGqnChLI72sa6wYiGqLzeaNA+2TdOiwSxNC/SZOT+7ujRUKlu6JvKkOqOms6G5n9ZPdXBsdfjUZJqjNj4oyAVRMdkuDVpcYlMi64ByiQ3sxLWoZIybW6TM0dwpleeBfeweFJ0KnahdA5jZWEX9uAAHDiCElxCGVxggPAIz/Bi3VpP1qv1Ni7NWJOebfgj6/0H1sSQ8A==</latexit><latexit sha1_base64="iJYvevAKnnZQIj8vcz4UXcngUcs=">AAAB53icbVBNS8NAEJ34WetX1aOXxSJ4KokX9VYQQfDSgrGFNpTNdtKu3WzC7kYoob/AiwcVr/4lb/4bt20O2vpg4PHeDDPzwlRwbVz321lZXVvf2Cxtlbd3dvf2KweHDzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH11O/9YRK80Tem3GKQUwHkkecUWOl5l2vUnVr7gxkmXgFqUKBRq/y1e0nLItRGiao1h3PTU2QU2U4EzgpdzONKWUjOsCOpZLGqIN8duiEnFqlT6JE2ZKGzNTfEzmNtR7Hoe2MqRnqRW8q/ud1MhNdBjmXaWZQsvmiKBPEJGT6NelzhcyIsSWUKW5vJWxIFWXGZlO2IXiLLy8T/7x2VfOabrV+U6RRgmM4gTPw4ALqcAsN8IEBwjO8wpvz6Lw4787HvHXFKWaO4A+czx8QP4yi</latexit>

⇠=<latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit>

⇠=<latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit><latexit sha1_base64="JiAdaEhNHNrB6pbnIyTdBEZj2Zc=">AAAB63icbVA9TwJBEJ3DL8Qv1NJmIzGxInc2YkdiY4mJJyRwIXvLHGzY273s7pkQwm+wsVBj6x+y89+4wBUKvmSSl/dmMjMvzgQ31ve/vdLG5tb2Tnm3srd/cHhUPT55NCrXDEOmhNKdmBoUXGJouRXYyTTSNBbYjse3c7/9hNpwJR/sJMMopUPJE86odVLYY0oO+9WaX/cXIOskKEgNCrT61a/eQLE8RWmZoMZ0Az+z0ZRqy5nAWaWXG8woG9Mhdh2VNEUTTRfHzsiFUwYkUdqVtGSh/p6Y0tSYSRq7zpTakVn15uJ/Xje3SSOacpnlFiVbLkpyQawi88/JgGtkVkwcoUxzdythI6opsy6figshWH15nYRX9Zt6cO/Xmo0ijTKcwTlcQgDX0IQ7aEEIDDg8wyu8edJ78d69j2VryStmTuEPvM8fPSiOdQ==</latexit>

KhX,Y |XY = 1i<latexit sha1_base64="q/vzHXuI2tXLRVTznUbFqbVG/OM=">AAACAHicbVBNS8NAEN34WetX1YvgZbEIHqQkXqwHoeBF8FLB2JQmlM122i7dbMLuRiixXvwrXjyoePVnePPfuE170NYHA2/fm2FnXphwprRtf1sLi0vLK6uFteL6xubWdmln907FqaTg0pjH0guJAs4EuJppDl4igUQhh0Y4uBz7jXuQisXiVg8TCCLSE6zLKNFGapf2r31ORI8D9k6aD17zwvFl/m6XynbFzoHniTMlZTRFvV368jsxTSMQmnKiVMuxEx1kRGpGOYyKfqogIXRAetAyVJAIVJDlF4zwkVE6uBtLU0LjXP09kZFIqWEUms6I6L6a9cbif14r1d1qkDGRpBoEnXzUTTnWMR7HgTtMAtV8aAihkpldMe0TSag2oRVNCM7syfPEPa2cV5wbu1yrTtMooAN0iI6Rg85QDV2hOnIRRY/oGb2iN+vJerHerY9J64I1ndlDf2B9/gCrpZXo</latexit><latexit sha1_base64="q/vzHXuI2tXLRVTznUbFqbVG/OM=">AAACAHicbVBNS8NAEN34WetX1YvgZbEIHqQkXqwHoeBF8FLB2JQmlM122i7dbMLuRiixXvwrXjyoePVnePPfuE170NYHA2/fm2FnXphwprRtf1sLi0vLK6uFteL6xubWdmln907FqaTg0pjH0guJAs4EuJppDl4igUQhh0Y4uBz7jXuQisXiVg8TCCLSE6zLKNFGapf2r31ORI8D9k6aD17zwvFl/m6XynbFzoHniTMlZTRFvV368jsxTSMQmnKiVMuxEx1kRGpGOYyKfqogIXRAetAyVJAIVJDlF4zwkVE6uBtLU0LjXP09kZFIqWEUms6I6L6a9cbif14r1d1qkDGRpBoEnXzUTTnWMR7HgTtMAtV8aAihkpldMe0TSag2oRVNCM7syfPEPa2cV5wbu1yrTtMooAN0iI6Rg85QDV2hOnIRRY/oGb2iN+vJerHerY9J64I1ndlDf2B9/gCrpZXo</latexit><latexit sha1_base64="q/vzHXuI2tXLRVTznUbFqbVG/OM=">AAACAHicbVBNS8NAEN34WetX1YvgZbEIHqQkXqwHoeBF8FLB2JQmlM122i7dbMLuRiixXvwrXjyoePVnePPfuE170NYHA2/fm2FnXphwprRtf1sLi0vLK6uFteL6xubWdmln907FqaTg0pjH0guJAs4EuJppDl4igUQhh0Y4uBz7jXuQisXiVg8TCCLSE6zLKNFGapf2r31ORI8D9k6aD17zwvFl/m6XynbFzoHniTMlZTRFvV368jsxTSMQmnKiVMuxEx1kRGpGOYyKfqogIXRAetAyVJAIVJDlF4zwkVE6uBtLU0LjXP09kZFIqWEUms6I6L6a9cbif14r1d1qkDGRpBoEnXzUTTnWMR7HgTtMAtV8aAihkpldMe0TSag2oRVNCM7syfPEPa2cV5wbu1yrTtMooAN0iI6Rg85QDV2hOnIRRY/oGb2iN+vJerHerY9J64I1ndlDf2B9/gCrpZXo</latexit><latexit sha1_base64="q/vzHXuI2tXLRVTznUbFqbVG/OM=">AAACAHicbVBNS8NAEN34WetX1YvgZbEIHqQkXqwHoeBF8FLB2JQmlM122i7dbMLuRiixXvwrXjyoePVnePPfuE170NYHA2/fm2FnXphwprRtf1sLi0vLK6uFteL6xubWdmln907FqaTg0pjH0guJAs4EuJppDl4igUQhh0Y4uBz7jXuQisXiVg8TCCLSE6zLKNFGapf2r31ORI8D9k6aD17zwvFl/m6XynbFzoHniTMlZTRFvV368jsxTSMQmnKiVMuxEx1kRGpGOYyKfqogIXRAetAyVJAIVJDlF4zwkVE6uBtLU0LjXP09kZFIqWEUms6I6L6a9cbif14r1d1qkDGRpBoEnXzUTTnWMR7HgTtMAtV8aAihkpldMe0TSag2oRVNCM7syfPEPa2cV5wbu1yrTtMooAN0iI6Rg85QDV2hOnIRRY/oGb2iN+vJerHerY9J64I1ndlDf2B9/gCrpZXo</latexit>

K<latexit sha1_base64="+k7vdyiaXvTSeWdlB7nWVXWB4M8=">AAAB53icbZA9SwNBEIbn4leMX1FLm8MgWIU7G7UyIKJgk4BnAskR9jZzyZq9vWN3TwhHfoGNhYqt/8Ta0s7Sf+Lmo9DEFxYe3neGnZkg4Uxpx/mycguLS8sr+dXC2vrG5lZxe+dWxamk6NGYx7IREIWcCfQ00xwbiUQSBRzrQf98lNfvUSoWixs9SNCPSFewkFGijVW7bhdLTtkZy54Hdwqls4/vy3cAqLaLn61OTNMIhaacKNV0nUT7GZGaUY7DQitVmBDaJ11sGhQkQuVn40GH9oFxOnYYS/OEtsfu746MREoNosBURkT31Gw2Mv/LmqkOT/yMiSTVKOjkozDlto7t0dZ2h0mkmg8MECqZmdWmPSIJ1eY2BXMEd3blefCOyqdlt+aUKhcwUR72YB8OwYVjqMAVVMEDCggP8ATP1p31aL1Yr5PSnDXt2YU/st5+AAbFj5M=</latexit><latexit sha1_base64="9iKOadZRBrr6lBxD+k88A0TZqfM=">AAAB53icbZC7SgNBFIbPxluMt3jpbAaDYBV2bdTKgIiCTQKuCSRLmJ2cTUZnL8zMCjHkCWwsVGx9AR/E0s4yb+LkUmjiDwMf/38Oc87xE8GVtu1vKzM3v7C4lF3OrayurW/kN7duVJxKhi6LRSxrPlUoeISu5lpgLZFIQ19g1b87G+bVe5SKx9G17ibohbQd8YAzqo1VuWrmC3bRHonMgjOBwunn4OJj52FQbua/Gq2YpSFGmgmqVN2xE+31qNScCeznGqnChLI72sa6wYiGqLzeaNA+2TdOiwSxNC/SZOT+7ujRUKlu6JvKkOqOms6G5n9ZPdXBsdfjUZJqjNj4oyAVRMdkuDVpcYlMi64ByiQ3sxLWoZIybW6TM0dwpleeBfeweFJ0KnahdA5jZWEX9uAAHDiCElxCGVxggPAIz/Bi3VpP1qv1Ni7NWJOebfgj6/0H1sSQ8A==</latexit><latexit sha1_base64="9iKOadZRBrr6lBxD+k88A0TZqfM=">AAAB53icbZC7SgNBFIbPxluMt3jpbAaDYBV2bdTKgIiCTQKuCSRLmJ2cTUZnL8zMCjHkCWwsVGx9AR/E0s4yb+LkUmjiDwMf/38Oc87xE8GVtu1vKzM3v7C4lF3OrayurW/kN7duVJxKhi6LRSxrPlUoeISu5lpgLZFIQ19g1b87G+bVe5SKx9G17ibohbQd8YAzqo1VuWrmC3bRHonMgjOBwunn4OJj52FQbua/Gq2YpSFGmgmqVN2xE+31qNScCeznGqnChLI72sa6wYiGqLzeaNA+2TdOiwSxNC/SZOT+7ujRUKlu6JvKkOqOms6G5n9ZPdXBsdfjUZJqjNj4oyAVRMdkuDVpcYlMi64ByiQ3sxLWoZIybW6TM0dwpleeBfeweFJ0KnahdA5jZWEX9uAAHDiCElxCGVxggPAIz/Bi3VpP1qv1Ni7NWJOebfgj6/0H1sSQ8A==</latexit><latexit sha1_base64="iJYvevAKnnZQIj8vcz4UXcngUcs=">AAAB53icbVBNS8NAEJ34WetX1aOXxSJ4KokX9VYQQfDSgrGFNpTNdtKu3WzC7kYoob/AiwcVr/4lb/4bt20O2vpg4PHeDDPzwlRwbVz321lZXVvf2Cxtlbd3dvf2KweHDzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH11O/9YRK80Tem3GKQUwHkkecUWOl5l2vUnVr7gxkmXgFqUKBRq/y1e0nLItRGiao1h3PTU2QU2U4EzgpdzONKWUjOsCOpZLGqIN8duiEnFqlT6JE2ZKGzNTfEzmNtR7Hoe2MqRnqRW8q/ud1MhNdBjmXaWZQsvmiKBPEJGT6NelzhcyIsSWUKW5vJWxIFWXGZlO2IXiLLy8T/7x2VfOabrV+U6RRgmM4gTPw4ALqcAsN8IEBwjO8wpvz6Lw4787HvHXFKWaO4A+czx8QP4yi</latexit>

Page 17: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Principal ideal ring[Abrams, Mantese, - ’18]

Let E be any graph. Then the associated Leavitt path algebra is a principal ideal ring if and only if E is finite and no cycle in E has an exit.

Structure of projective modulesAlbrecht ’61. Each projective left module over a left semi-hereditary unital ring is isomorphic to a direct sum of finitely generated left ideals.

Let be a finite graph and any field. Any projective left module is isomorphic to a direct sum of prin-cipal left ideals.

E<latexit sha1_base64="HpzEzVQ2aDUuKINpauaS1FB7M20=">AAAB53icbVBNS8NAEJ34WetX1aOXxSJ4KokX9VaQgscWjC20oWy2k3btZhN2N0IJ/QVePKh49S9589+4bXPQ1gcDj/dmmJkXpoJr47rfztr6xubWdmmnvLu3f3BYOTp+0EmmGPosEYnqhFSj4BJ9w43ATqqQxqHAdji+nfntJ1SaJ/LeTFIMYjqUPOKMGiu1Gv1K1a25c5BV4hWkCgWa/cpXb5CwLEZpmKBadz03NUFOleFM4LTcyzSmlI3pELuWShqjDvL5oVNybpUBiRJlSxoyV39P5DTWehKHtjOmZqSXvZn4n9fNTHQd5FymmUHJFouiTBCTkNnXZMAVMiMmllCmuL2VsBFVlBmbTdmG4C2/vEr8y9pNzWu51XqjSKMEp3AGF+DBFdThDprgAwOEZ3iFN+fReXHenY9F65pTzJzAHzifPwctjJw=</latexit><latexit sha1_base64="HpzEzVQ2aDUuKINpauaS1FB7M20=">AAAB53icbVBNS8NAEJ34WetX1aOXxSJ4KokX9VaQgscWjC20oWy2k3btZhN2N0IJ/QVePKh49S9589+4bXPQ1gcDj/dmmJkXpoJr47rfztr6xubWdmmnvLu3f3BYOTp+0EmmGPosEYnqhFSj4BJ9w43ATqqQxqHAdji+nfntJ1SaJ/LeTFIMYjqUPOKMGiu1Gv1K1a25c5BV4hWkCgWa/cpXb5CwLEZpmKBadz03NUFOleFM4LTcyzSmlI3pELuWShqjDvL5oVNybpUBiRJlSxoyV39P5DTWehKHtjOmZqSXvZn4n9fNTHQd5FymmUHJFouiTBCTkNnXZMAVMiMmllCmuL2VsBFVlBmbTdmG4C2/vEr8y9pNzWu51XqjSKMEp3AGF+DBFdThDprgAwOEZ3iFN+fReXHenY9F65pTzJzAHzifPwctjJw=</latexit><latexit sha1_base64="HpzEzVQ2aDUuKINpauaS1FB7M20=">AAAB53icbVBNS8NAEJ34WetX1aOXxSJ4KokX9VaQgscWjC20oWy2k3btZhN2N0IJ/QVePKh49S9589+4bXPQ1gcDj/dmmJkXpoJr47rfztr6xubWdmmnvLu3f3BYOTp+0EmmGPosEYnqhFSj4BJ9w43ATqqQxqHAdji+nfntJ1SaJ/LeTFIMYjqUPOKMGiu1Gv1K1a25c5BV4hWkCgWa/cpXb5CwLEZpmKBadz03NUFOleFM4LTcyzSmlI3pELuWShqjDvL5oVNybpUBiRJlSxoyV39P5DTWehKHtjOmZqSXvZn4n9fNTHQd5FymmUHJFouiTBCTkNnXZMAVMiMmllCmuL2VsBFVlBmbTdmG4C2/vEr8y9pNzWu51XqjSKMEp3AGF+DBFdThDprgAwOEZ3iFN+fReXHenY9F65pTzJzAHzifPwctjJw=</latexit><latexit sha1_base64="HpzEzVQ2aDUuKINpauaS1FB7M20=">AAAB53icbVBNS8NAEJ34WetX1aOXxSJ4KokX9VaQgscWjC20oWy2k3btZhN2N0IJ/QVePKh49S9589+4bXPQ1gcDj/dmmJkXpoJr47rfztr6xubWdmmnvLu3f3BYOTp+0EmmGPosEYnqhFSj4BJ9w43ATqqQxqHAdji+nfntJ1SaJ/LeTFIMYjqUPOKMGiu1Gv1K1a25c5BV4hWkCgWa/cpXb5CwLEZpmKBadz03NUFOleFM4LTcyzSmlI3pELuWShqjDvL5oVNybpUBiRJlSxoyV39P5DTWehKHtjOmZqSXvZn4n9fNTHQd5FymmUHJFouiTBCTkNnXZMAVMiMmllCmuL2VsBFVlBmbTdmG4C2/vEr8y9pNzWu51XqjSKMEp3AGF+DBFdThDprgAwOEZ3iFN+fReXHenY9F65pTzJzAHzifPwctjJw=</latexit>

K<latexit sha1_base64="iJYvevAKnnZQIj8vcz4UXcngUcs=">AAAB53icbVBNS8NAEJ34WetX1aOXxSJ4KokX9VYQQfDSgrGFNpTNdtKu3WzC7kYoob/AiwcVr/4lb/4bt20O2vpg4PHeDDPzwlRwbVz321lZXVvf2Cxtlbd3dvf2KweHDzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH11O/9YRK80Tem3GKQUwHkkecUWOl5l2vUnVr7gxkmXgFqUKBRq/y1e0nLItRGiao1h3PTU2QU2U4EzgpdzONKWUjOsCOpZLGqIN8duiEnFqlT6JE2ZKGzNTfEzmNtR7Hoe2MqRnqRW8q/ud1MhNdBjmXaWZQsvmiKBPEJGT6NelzhcyIsSWUKW5vJWxIFWXGZlO2IXiLLy8T/7x2VfOabrV+U6RRgmM4gTPw4ALqcAsN8IEBwjO8wpvz6Lw4787HvHXFKWaO4A+czx8QP4yi</latexit><latexit sha1_base64="iJYvevAKnnZQIj8vcz4UXcngUcs=">AAAB53icbVBNS8NAEJ34WetX1aOXxSJ4KokX9VYQQfDSgrGFNpTNdtKu3WzC7kYoob/AiwcVr/4lb/4bt20O2vpg4PHeDDPzwlRwbVz321lZXVvf2Cxtlbd3dvf2KweHDzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH11O/9YRK80Tem3GKQUwHkkecUWOl5l2vUnVr7gxkmXgFqUKBRq/y1e0nLItRGiao1h3PTU2QU2U4EzgpdzONKWUjOsCOpZLGqIN8duiEnFqlT6JE2ZKGzNTfEzmNtR7Hoe2MqRnqRW8q/ud1MhNdBjmXaWZQsvmiKBPEJGT6NelzhcyIsSWUKW5vJWxIFWXGZlO2IXiLLy8T/7x2VfOabrV+U6RRgmM4gTPw4ALqcAsN8IEBwjO8wpvz6Lw4787HvHXFKWaO4A+czx8QP4yi</latexit><latexit sha1_base64="iJYvevAKnnZQIj8vcz4UXcngUcs=">AAAB53icbVBNS8NAEJ34WetX1aOXxSJ4KokX9VYQQfDSgrGFNpTNdtKu3WzC7kYoob/AiwcVr/4lb/4bt20O2vpg4PHeDDPzwlRwbVz321lZXVvf2Cxtlbd3dvf2KweHDzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH11O/9YRK80Tem3GKQUwHkkecUWOl5l2vUnVr7gxkmXgFqUKBRq/y1e0nLItRGiao1h3PTU2QU2U4EzgpdzONKWUjOsCOpZLGqIN8duiEnFqlT6JE2ZKGzNTfEzmNtR7Hoe2MqRnqRW8q/ud1MhNdBjmXaWZQsvmiKBPEJGT6NelzhcyIsSWUKW5vJWxIFWXGZlO2IXiLLy8T/7x2VfOabrV+U6RRgmM4gTPw4ALqcAsN8IEBwjO8wpvz6Lw4787HvHXFKWaO4A+czx8QP4yi</latexit><latexit sha1_base64="iJYvevAKnnZQIj8vcz4UXcngUcs=">AAAB53icbVBNS8NAEJ34WetX1aOXxSJ4KokX9VYQQfDSgrGFNpTNdtKu3WzC7kYoob/AiwcVr/4lb/4bt20O2vpg4PHeDDPzwlRwbVz321lZXVvf2Cxtlbd3dvf2KweHDzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH11O/9YRK80Tem3GKQUwHkkecUWOl5l2vUnVr7gxkmXgFqUKBRq/y1e0nLItRGiao1h3PTU2QU2U4EzgpdzONKWUjOsCOpZLGqIN8duiEnFqlT6JE2ZKGzNTfEzmNtR7Hoe2MqRnqRW8q/ud1MhNdBjmXaWZQsvmiKBPEJGT6NelzhcyIsSWUKW5vJWxIFWXGZlO2IXiLLy8T/7x2VfOabrV+U6RRgmM4gTPw4ALqcAsN8IEBwjO8wpvz6Lw4787HvHXFKWaO4A+czx8QP4yi</latexit>

LK(E)-<latexit sha1_base64="l0TXFnPUY+TcChg3vEfVA9vEuWw=">AAAB9HicbVBNS8NAEJ34WetX1aOXYBHqwZJ4UW8FKQh6qGBsoY1ls922SzebsDtRS+j/8OJBxas/xpv/xm2bg7Y+GHi8N8PMvCAWXKPjfFsLi0vLK6u5tfz6xubWdmFn905HiaLMo5GIVCMgmgkumYccBWvEipEwEKweDC7Gfv2BKc0jeYvDmPkh6Une5ZSgke6v21el6lEL2ROmx6N2oeiUnQnseeJmpAgZau3CV6sT0SRkEqkgWjddJ0Y/JQo5FWyUbyWaxYQOSI81DZUkZNpPJ1eP7EOjdOxupExJtCfq74mUhFoPw8B0hgT7etYbi/95zQS7Z37KZZwgk3S6qJsIGyN7HIHd4YpRFENDCFXc3GrTPlGEogkqb0JwZ1+eJ95J+bzs3jjFSjVLIwf7cAAlcOEUKnAJNfCAgoJneIU369F6sd6tj2nrgpXN7MEfWJ8/5VGRqw==</latexit><latexit sha1_base64="l0TXFnPUY+TcChg3vEfVA9vEuWw=">AAAB9HicbVBNS8NAEJ34WetX1aOXYBHqwZJ4UW8FKQh6qGBsoY1ls922SzebsDtRS+j/8OJBxas/xpv/xm2bg7Y+GHi8N8PMvCAWXKPjfFsLi0vLK6u5tfz6xubWdmFn905HiaLMo5GIVCMgmgkumYccBWvEipEwEKweDC7Gfv2BKc0jeYvDmPkh6Une5ZSgke6v21el6lEL2ROmx6N2oeiUnQnseeJmpAgZau3CV6sT0SRkEqkgWjddJ0Y/JQo5FWyUbyWaxYQOSI81DZUkZNpPJ1eP7EOjdOxupExJtCfq74mUhFoPw8B0hgT7etYbi/95zQS7Z37KZZwgk3S6qJsIGyN7HIHd4YpRFENDCFXc3GrTPlGEogkqb0JwZ1+eJ95J+bzs3jjFSjVLIwf7cAAlcOEUKnAJNfCAgoJneIU369F6sd6tj2nrgpXN7MEfWJ8/5VGRqw==</latexit><latexit sha1_base64="l0TXFnPUY+TcChg3vEfVA9vEuWw=">AAAB9HicbVBNS8NAEJ34WetX1aOXYBHqwZJ4UW8FKQh6qGBsoY1ls922SzebsDtRS+j/8OJBxas/xpv/xm2bg7Y+GHi8N8PMvCAWXKPjfFsLi0vLK6u5tfz6xubWdmFn905HiaLMo5GIVCMgmgkumYccBWvEipEwEKweDC7Gfv2BKc0jeYvDmPkh6Une5ZSgke6v21el6lEL2ROmx6N2oeiUnQnseeJmpAgZau3CV6sT0SRkEqkgWjddJ0Y/JQo5FWyUbyWaxYQOSI81DZUkZNpPJ1eP7EOjdOxupExJtCfq74mUhFoPw8B0hgT7etYbi/95zQS7Z37KZZwgk3S6qJsIGyN7HIHd4YpRFENDCFXc3GrTPlGEogkqb0JwZ1+eJ95J+bzs3jjFSjVLIwf7cAAlcOEUKnAJNfCAgoJneIU369F6sd6tj2nrgpXN7MEfWJ8/5VGRqw==</latexit><latexit sha1_base64="l0TXFnPUY+TcChg3vEfVA9vEuWw=">AAAB9HicbVBNS8NAEJ34WetX1aOXYBHqwZJ4UW8FKQh6qGBsoY1ls922SzebsDtRS+j/8OJBxas/xpv/xm2bg7Y+GHi8N8PMvCAWXKPjfFsLi0vLK6u5tfz6xubWdmFn905HiaLMo5GIVCMgmgkumYccBWvEipEwEKweDC7Gfv2BKc0jeYvDmPkh6Une5ZSgke6v21el6lEL2ROmx6N2oeiUnQnseeJmpAgZau3CV6sT0SRkEqkgWjddJ0Y/JQo5FWyUbyWaxYQOSI81DZUkZNpPJ1eP7EOjdOxupExJtCfq74mUhFoPw8B0hgT7etYbi/95zQS7Z37KZZwgk3S6qJsIGyN7HIHd4YpRFENDCFXc3GrTPlGEogkqb0JwZ1+eJ95J+bzs3jjFSjVLIwf7cAAlcOEUKnAJNfCAgoJneIU369F6sd6tj2nrgpXN7MEfWJ8/5VGRqw==</latexit>

[Abrams, Mantese, - ’18]

Page 18: Leavitt path algebras are Bézout - University of Manchester · 2018-09-11 · Leavitt path algebras are Bézout Alberto Tonolo, Università di Padova Conference in memory of Gena

Thank you for your attention!