Algèbre Homologique des <i>N</i>-Complexes et Homologie de Hochschild aux Racines de l'Unité

Abstract

We set up a homological algebra for N-complexes, which are graded modules together with a degree —1 endomorphism d satisfying d__N = 0. We define Tor- and Ext-groups for N-complexes and we compute them m terms of their classical counterparts (N = 2) As an application, we get an alternative définition of thé Hochschild homology of an associative algebra out of an N-complex whose differential is based on a primitive N-th root of unity.