Homologie de l'algèbre quantique des symboles pseudo-différentiels sur le cercle.

Marc Wambst (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Let $\Psi_q$ be the quantum algebra of pseudo-differential symbols on the circle. We construct quasi-isomorphisms between the standard Hochschild complex of $\Psi_q$ and ``small'' complexes. We deduce the Hochschid homology and the first cyclic homology groups of $\Psi_q$. These constructions give naturally rise to two cyclic 1-cocycles which turn out to be the Lie cocycles constructed by Khesin, Lyubashenko and Roger. All homology groups considered here are topological in an appropriate sense.

Mots clés: cyclic homology; quantum algebras; "cyclic homology; Hochschild homology; pseudodifferential symbols; quantum algebras"

Domaines: Anneaux et algèbres [math.RA]

Marc Wambst. Homologie de l'algèbre quantique des symboles pseudo-différentiels sur le cercle.. 1995. ⟨hal-00129713⟩