Higher Dimensional Peiffer Elements in Simplicial Commutative Algebras

Z. Arvasi and T. Porter

Let E be a simplicial commutative algebra such that E_n is generated by degenerate elements. It is shown that in this case the n^th term of the Moore complex of E is generated by images of certain pairings from lower dimensions. This is then used to give a description of the boundaries in dimension n-1 for n = 2, 3, and 4.

Keywords: Simplicial commutative algebra, boundaries, Moore complex .

1991 MSC: 18G30, 18G55, 16E99 .

Theory and Applications of Categories, Vol. 3, 1997, No. 1, pp 1-23.


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