Property (T) for locally compact groups and C*-algebras - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2019

Property (T) for locally compact groups and C*-algebras

Bachir Bekka
  • Fonction : Auteur
  • PersonId : 867269
Chi-Keung Ng
  • Fonction : Auteur
  • PersonId : 1029883

Résumé

Let G be a locally compact group and let C∗(G) and C∗r(G) be the full group C∗-algebra and the reduced group C∗-algebra of G. We investigate the relationship between Property (T) for G and Property (T) as well as its strong version for C∗(G) and C∗r(G). We show that G has Property (T) if (and only if) C∗(G) has Property (T). In the case where G is a locally compact IN-group, we prove that G has Property (T) if and only if C∗r(G) has strong Property (T). We also show that C∗r(G) has strong Property (T) for every non-amenable locally compact group G for which C∗r(G) is nuclear. Some of these groups (as for instance G=SL2(R)) do not have Property T.
Fichier principal
Vignette du fichier
prop-t-c-st-alg-and-gp-3g.pdf (332.32 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01745801 , version 1 (28-03-2018)

Identifiants

  • HAL Id : hal-01745801 , version 1

Citer

Bachir Bekka, Chi-Keung Ng. Property (T) for locally compact groups and C*-algebras. Proceedings of the American Mathematical Society, 2019, 147 (5), pp.2159-2169. ⟨hal-01745801⟩
282 Consultations
392 Téléchargements

Partager

Gmail Facebook X LinkedIn More