Marc Wambst

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

 Bull. Soc. Math. France 124,  (1996), no. 3, 523-544.

Abstract : 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-clé, Keywords : cyclic homology, Hochschild homology, pseudodifferential symbols, quantum algebras

Classifications : 16E40, 16S32,81S05

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