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Morphisme de Baum-Connes tordu par une représentation non unitaire

Published online by Cambridge University Press:  08 December 2009

Maria Paula Gomez-Aparicio
Maria Paula Gomez-Aparicio
Affiliation:
Institut de Mathématiques de Jussieu, Projet d'algèbres d'Opérateurs et représentations, 175 rue du chevaleret, 75013 Paris, France. gomez@math.jussieu.fr
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Abstract

Let G be a locally compact group and ρ a non-unitary finite dimensional representation of G. We consider tensor products of ρ by some unitary representations of G in order to define two Banach algebras analogous to the group C*-algebras, C*(G) and C*r(G). We calculate the K-theory of such algebras for a large class of groups satisfying the Baum-Connes conjecture.

Soit G un groupe localement compact et ρ une représentation de dimension finie de G non unitaire. On définit des algèbres de Banach analogues aux C*-algèbres de groupe, C*(G) et C*r(G), en considérant l'ensemble des représentations de la forme ρ ⊗ π, où π parcourt un ensemble de représentations unitaires de G. On calcule la K-théorie de ces algèbres pour une large classe de groupes vérifiant la conjecture de Baum-Connes.

Keywords

Non-unitary representationsBanach algebrasKK-theoryBaum-Connes conjecture
Type
Research Article
Information
Journal of K-Theory , Volume 6 , Issue 1 , August 2010 , pp. 23 - 68
Copyright
Copyright © ISOPP 2009

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