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Comptes Rendus Mathématique
Volume 341, n° 4
pages 217-222 (août 2005)
Doi : 10.1016/j.crma.2005.07.002
Received : 13 April 2005 ;  accepted : 7 June 2005
Semi-exactitude du bifoncteur de Kasparov pour les actions moyennables
Half-exactness of the Kasparov equivariant bifunctor for amenable actions
 

Driss El Morsli
Institut de mathématiques de Luminy, 163, avenue de Luminy, case 907, 13288 Marseille cedex 9, France 

Résumé

Soit une suite exacte équivariante de G -algèbres séparables  -graduées, admettant un relèvement complètement positif gradué (non nécessairement équivariant) de norme 1. Nous utilisons la notation   pour un groupe de transformation topologique moyennable au sens dʼAnantharaman-Delaroche. Nous établissons un isomorphisme concernant le bifoncteur equivariant de Kasparov  . Cet isomorphisme en K -théorie, permet dʼétendre la semi-exactitude du cas des algèbres propres (cette dernière est analogue à celle obtenue par Skandalis dans le cas non-equivariant) à celui des actions moyennables. En particulier, nous nous plaçons dans un cas important, celui des déplacements hyperboliques de la géométrie de Poincaré-Lobatschevsky sur le disque unité. Pour citer cet article : D. El Morsli, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Abstract

Consider an equivariant extension of graded separable G -algebras which admits a completely linear positive, grading preserving cross section (not necessary equivariant) of norm 1. We denote   an amenable topological transformation group in the sense of Anantharaman-Delaroche. We establish an isomorphism concerning the Kasparov equivariant bifunctor  . This isomorphism in K -theory, allows one to extend the half-exactness from the case of the proper algebras (which is analogue to the one obtained by Skandalis in the non-equivariant case) to the case of amenable actions. In particular, we will place ourselves in a significant case, that of hyperbolic displacements of the Poincaré-Lobatschevsky geometry on the unit disc. To cite this article: D. El Morsli, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.


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