Algèbre homologique des N-complexes et homologie de Hochschild aux racines de l'unité

Christian Kassel (1) , Marc Wambst (1)

1 IRMA - Institut de Recherche Mathématique Avancée

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 in terms of their classical counterparts (N = 2). As an application, we get an alternative definition of the Hochschild homology of an associative algebra out of an N-complex whose differential is based on a primitive N-th root of unity.

Mots clés: homological algebra; Hochschild homology; simplicial module; q-calculus

Domaines: Algèbres quantiques [math.QA]

Christian Kassel, Marc Wambst. Algèbre homologique des N-complexes et homologie de Hochschild aux racines de l'unité. Publ. Res. Inst. Math. Sci. Kyoto University, 1998, 34, pp.91-114. ⟨hal-00124665⟩