Seminario de Algebra e Logica (CMA/FCT)

Tıtulo: “From Simplicial Homotopy to 2-Crossed Module Homotopy”

Orador: Kadir EMIR (Research Assistant, Dept. of Mathematics - Computer Sciences,Eskisehir Osmangazi University, TURKEY)

Data: 16/04/2014 (4a feira)

Local e Hora: Sala 1.4 Ed. VII as 14 horas

Resumo: As is known from [1, 4, 7], simplicial algebras with Moore complex of length1 (2) lead to crossed (2-crossed) modules that are related to Kozsul complex and Andre-Quillen homology constructions for use in homotopical and homological algebra. Doncel,Grandjean and Vale extended the 2-crossed modules of groups to commutative algebras in[3]. Homotopy of crossed complex morphisms on groupoids was first introduced by Brownand Higgins in [2]. Homotopy of 2-crossed module morphisms on groups was defined byMartins and Gohla in [5, 6]. In this study, we will try to define the homotopy of crossed(2-crossed) module morphisms on commutative algebras. Upon this, we will try to define amap that carries the homotopy from simplicial algebras to crossed (2-crossed) module, as apart of the functor between them.

Referencias

[1] Arvasi Z., Porter T., Higher Dimensional Peiffer Elements in Simplicial Commutative Algebras,TAC, 1997.

[2] Brown R., Higgins P.J., Tensor Products and Homotopies for ω-Groupoids and Crossed Complexes,Journal of Pure and Applied Algebra, 1987.

[3] Doncel J.L., Grandjean A.R. , Vale M.L., On the Homology of Commutative Algebras, Journalof Pure and Applied Algebra, 1992.

[4] Grandjean A.R. , Vale M.L., 2-Modulos Cruzados en la Cohomologia de Andre-Quillen Memoriasde la Real Academia de Ciencias, 1986.

[5] Martins J.F., Gohla B., Pointed Homotopy and Pointed Lax Homotopy of 2-Crossed Module Maps,Advances in Mathematics, 2011.

[6] Martins J.F., The Fundamental 2-Crossed Complex of a Reduced CW-Complex, Homology, Homotopyand Applications, 2013.

[7] Porter T., Homology of commutative algebras and an invariant of Simis and Vasconceles. Journal ofAlgebra, 1987.