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

Pierrot, François

doi:10.5802/aif.1919

Structure de certaines

C^{*}

-algèbres associées aux réseaux de

{PSL}_{2} (ℝ)

[ On the structure of certain

C^{*}

-algebra associated to lattices of

{PSL}_{2} (ℝ)

]

Pierrot, François

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

Abstract
Résumé

By using the infinitesimal structure of the unitary irreducible representations of ${PSL}_{2} (ℝ)$ , we give a complete description of certain $C^{*}$ -algebras associated to lattices in ${PSL}_{2} (ℝ)$ ; this gives answers to some questions of Bekka–de La Harpe–Valette.

En utilisant la structure infinitésimale des représentations unitaires irréductibles de ${PSL}_{2} (ℝ)$ , nous donnons une description complète de certaines $C^{*}$ - algèbres associées aux réseaux de ${PSL}_{2} (ℝ)$ , répondant ainsi à certaines questions de Bekka–de La Harpe–Valette.

MR 1935551 | Zbl 1053.22004

DOI : https://doi.org/10.5802/aif.1919
Classification: 22D25, 43A15
Keywords:

C^{*}

-algebras, unitary representations,

(g, k)

-modules, lattices

@article{AIF_2002__52_5_1287_0,
     author = {Pierrot, Fran\c cois},
     title = {Structure de certaines $C^*$-alg\`ebres associ\'ees aux r\'eseaux de ${\rm PSL}\_2({\mathbb {R}})$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {52},
     number = {5},
     year = {2002},
     pages = {1287-1299},
     doi = {10.5802/aif.1919},
     zbl = {1053.22004},
     mrnumber = {1935551},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2002__52_5_1287_0}
}

Pierrot, François. Structure de certaines $C^*$-algèbres associées aux réseaux de ${\rm PSL}_2({\mathbb {R}})$. Annales de l'Institut Fourier, Volume 52 (2002) no. 5, pp. 1287-1299. doi : 10.5802/aif.1919. http://www.numdam.org/item/AIF_2002__52_5_1287_0/

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