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

Pierrot, François

Annales de l'Institut Fourier, Tome 52 (2002) no. 5, pp. 1287-1299

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

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

Classification : 22D25, 43A15
Mots-clés : $C^*$-algèbres, représentations unitaires, $(g,k)$-modules, réseaux
Keywords: $C^*$-algebras, unitary representations, $(g,k)$-modules, lattices

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