Affiliation:
1. KÜTAHYA DUMLUPINAR ÜNİVERSİTESİ
Abstract
In this paper, we describe the crossed corner of commutative algebras and present the relation between the category of crossed corners of commutative algebras and the category of reduced simplicial commutative algebras with Moore complex of length 2. We provide a passage from crossed corners to bisimplicial algebras. In this construction, we utilize the Artin-Mazur codiagonal functor from reduced bisimplicial algebras to simplicial algebras and the hypercrossed complex pairings in the Moore complex of a simplicial algebra. Using the coskeleton functor from the category of $k$-truncated simplicial algebras to the category simplicial algebras with Moore complex of length $k$, we see that the length of Moore complex of the reduced simplicial algebra obtained from a crossed corner is 2.
Subject
Geology,Ocean Engineering,Water Science and Technology
Reference19 articles.
1. J. H. C. Whitehead, Combinatorial Homotopy II, Bulletin of the American Mathematical Society 55 (1949) 453{--}496.
2. D. Guin-Wal\'{e}ry, J-L. Loday, Obsruction {\'{a}} l'excision en K-theories Alg{\'{e}}brique, in: E. M. Friedlander, M. R. Stein (Eds.), Algebraic K-Theory Evanston 1980, Vol. 854 of \emph{Lectute Notes Mathematics}, Springer, Berlin, 1981, pp. 179{--}216.
3. H. J. Baues, Combinatorial Homotopy and 4-Dimensional Complexes, Walter de Gruyter, Berlin, 1991.
4. Z. Arvasi, E. Ulualan, Quadratic and 2-Crossed Modules of Algebras, Algebra Colloquium 14 (2007) 669{--}686.
5. E. Ulualan, E. Uslu, Quadratic Modules for Lie Algebras, Hacettepe Journal of Mathematics and Statistics 40 (3) (2011) 409{--}419.