Applications of Peiffer pairings in the Moore complex of a simplicial group

A. Mutlu, T. Porter

Generalising a result of Brown and Loday, we give for n=3 and 4, a decomposition of the group, d_nNG_n, of boundaries of a simplicial group G as a product of commutator subgroups. Partial results are given for higher dimensions. Applications to 2-crossed modules and quadratic modules are discussed.

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Keywords: Simplicial groups, Brown-Loday lemma, Peiffer elements, 2-crossed modules.

1991 MSC: 18G30, 55U10, 55P10.

Theory and Applications of Categories, Vol. 4, 1998, No. 7, pp .148-173

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