Uniformly recurrent subgroups and simple C*-algebras

Elek, Gabor (2018) Uniformly recurrent subgroups and simple C*-algebras. Journal of Functional Analysis, 274 (6). pp. 1657-1689. ISSN 0022-1236

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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.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Functional Analysis
Additional Information:
This is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 274, 6, 2018 DOI: 10.1016/j.jfa.2018.01.004
Uncontrolled Keywords:
?? uniformly recurrent subgroupssimple c⁎-algebrasamenable tracesgraph limitsanalysis ??
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Deposited On:
11 Jan 2018 14:36
Last Modified:
29 Jan 2024 00:26