Dold-Kan correspondence for N-complexes

J.L. CASTIGLIONI

Colonia del Sacramento, R. O. del Uruguay

Congreso; XVI Coloquio Latinoamericano de Algebra; 2005

Centro de Matemática - Facultad de Ciencias- U. de la República.

N-complexes were introduced by M. M. Kapranov [arXiv:q-alg/9611005] and extensively studied by M. Dubois-Violette [K-theory 14: 371-404]. Several ways of associate an N-(co)chain complex to a (co)simplicial module were proposed in the latter. However, no analog of the Dold-Kan correspondence can be found in the literature. In this talk we established a correspondence between the category of N-(co)chain complexes and an appropriate subcategory of (co)simplicial modules. Some applications of this result were developed.