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.
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Christian Kassel, Marc Wambst, Algèbre Homologique des <i>N</i>-Complexes et Homologie de Hochschild aux Racines de l'Unité. Publ. Res. Inst. Math. Sci. 34 (1998), no. 2, pp. 91–114DOI 10.2977/PRIMS/1195144755