Structure de certaines $C^*$-algèbres associées aux réseaux de ${\rm PSL}_2({\mathbb {R}})$

Pierrot, François

Annales de l'Institut Fourier, Tome 52 (2002), p. 1287-1299 / Harvested from Numdam

Résumé

En utilisant la structure infinitésimale des représentations unitaires irréductibles de ${\rm PSL}_2({\mathbb {R}})$, nous donnons une description complète de certaines $C^*$- algèbres associées aux réseaux de ${\rm PSL}_2({\mathbb {R}})$, répondant ainsi à certaines questions de Bekka–de La Harpe–Valette.

Abstract

By using the infinitesimal structure of the unitary irreducible representations of ${\rm PSL}_2({\mathbb {R}})$, we give a complete description of certain $C^*$-algebras associated to lattices in ${\rm PSL}_2({\mathbb {R}})$; this gives answers to some questions of Bekka–de La Harpe–Valette.

Détail

Publié le : 2002-01-01

MR 1935551 | Zbl 1053.22004

DOI : https://doi.org/10.5802/aif.1919
Classification:  22D25,  43A15
Mots clés: $C^*$-algèbres,représentations unitaires, $(g,k)$-modules, réseaux

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