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Uniformly recurrent subgroups and simple C*-algebras

Research output: Contribution to journalJournal article

E-pub ahead of print
<mark>Journal publication date</mark>9/01/2018
<mark>Journal</mark>Journal of Functional Analysis
Number of pages34
<mark>State</mark>E-pub ahead of print
Early online date9/01/18
<mark>Original language</mark>English

Abstract

We study uniformly recurrent subgroups (URS) introduced by Glasner and Weiss [18]. Answering their query we show that any URS Z of a finitely generated group is the stability system of a minimal Z-proper action. We also show that for any sofic URS Z there is a Z-proper action
admitting an invariant measure. We prove that for a URS Z all Z-proper actions admits an invariant measure if and only if Z is coamenable. In the second part of the paper we study the separable C*
-algebras associated to URS’s. We prove that if a URS is generic then its C*-algebra is simple.
We give various examples of generic URS’s with exact and nuclear C*-algebras and an example of a URS Z for which the associated simple C*-algebra is not exact and not even locally reflexive, in particular, it admits both a uniformly amenable trace and a nonuniformly amenable trace.