Quasi-regular representations of discrete groups and associated C*-algebras

Bachir Bekka (1) , Mehrdad Kalantar (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 University of Houston

Let G be a countable group. We introduce several equivalence relations on the set Sub(G) of subgroups of G, defined by properties of the quasi-regular representations λ G/H associated to H ∈ Sub(G) and compare them to the relation of G-conjugacy of subgroups. We define a class Sub sg (G) of subgroups (these are subgroups with a certain spectral gap property) and show that they are rigid, in the sense that the equivalence class of H ∈ Sub sg (G) for any one of the above equivalence relations coincides with the G-conjugacy class of H. Next, we introduce a second class Sub w−par (G) of subgroups (these are subgroups which are weakly parabolic in some sense) and we establish results concerning the ideal structure of the C

Domaines: Analyse fonctionnelle [math.FA]; Systèmes dynamiques [math.DS]

Bachir Bekka, Mehrdad Kalantar. Quasi-regular representations of discrete groups and associated C*-algebras. Transactions of the American Mathematical Society, 2020, 373 (3), pp.2105-2133. ⟨10.1090/tran/7969⟩. ⟨hal-02053208⟩