Affiliation:
1. KUTAHYA DUMLUPINAR UNIVERSITY
Abstract
A simplicial commutative algebra with Moore complex of length 1 gives a crossed module structure over commutative algebras. In this study, we will give 2-dimensional version of this result by giving hypercrossed complex pairings for a bisimplicial algebra and its Moore bicomplex. We give a detailed calculation in low dimensions for these pairings to see their role in the structures of crossed squares and bisimplicial algebras. In this context, we prove that if the Moore bicomplex of a bisimplicial commutative algebra is of length 1, then it gives a crossed square structure over commutative algebras.
Publisher
Fundamental Journal of Mathematics and Applications
Reference14 articles.
1. [1] A.R. Grandjean, M.J. Vale, 2-Modulos cruzados an la cohomologia de andr´e-quillen, Memorias de la Real Academia de Ciencias, 22 (1986), 1–28.
2. [2] D. Conduche, Modules crois´es c´en´eralis´es de longueur 2, J. Pure Appl. Algebra, 34 (1984), 155-178.
3. [3] D. Conduche, Simplicial crossed modules and mapping cones, Georgian Math. J., 10(4) (2003), 623-636.
4. [4] D. Guin-Wal´ery, J-L. Loday, Obsruction´a l’excision en K-theories Alg´ebrique, Evanston conference on Algebraic K-Theory 1980, (Lectute Notes
Mathematics) 854, 179-216, Berlin Heidelberg New York, Springer 1981.
5. [5] G.J. Ellis, Higher dimensional crossed modules of algebras, J. Pure Appl. Algebra, 52 (1988), 277-282.
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2 articles.
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