Peiffer Elements in Simplicial Groups and Algebras

Higher Dimensional Peiffer Elements in Simplicial Commutative Algebras

Let E be a simplicial commutative algebra such that En is generated by degenerate elements. It is shown that in this case the nth 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.

Higher Dimensional Peiffer Elements in Simplicial Commutative Algebras

Let E be a simplicial commutative algebra such that En is generated by degenerate elements. It is shown that in this case the nth 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.

On Isomorphism of Simplicial Complexes and Their Related Algebras

A pr 1 99 9 Iterated Peiffer pairings in the Moore complex of a simplicial group

We introduce a pairing structure within the Moore complex NG of a simplicial group G and use it to investigate generators for N G n ∩ D n where D n is the subgroup generated by degenerate elements. This is applied to the study of algebraic models for homotopy types.

00 4 v 1 1 8 M ay 1 99 4 Homology for Operator Algebras I : Spectral homology for reflexive algebras

England Abstract A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the simplicial homology of the underlying simplicial complex in the case of a digraph algebra. These groups are computable and useful. In parti...