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  • 1704.02595

    Rights statement: 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

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Uniformly recurrent subgroups and simple C*-algebras

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Uniformly recurrent subgroups and simple C*-algebras. / Elek, Gabor.

In: Journal of Functional Analysis, Vol. 274, No. 6, 15.03.2018, p. 1657-1689.

Research output: Contribution to journalJournal article

Harvard

Elek, G 2018, 'Uniformly recurrent subgroups and simple C*-algebras', Journal of Functional Analysis, vol. 274, no. 6, pp. 1657-1689. https://doi.org/10.1016/j.jfa.2018.01.004

APA

Vancouver

Elek G. Uniformly recurrent subgroups and simple C*-algebras. Journal of Functional Analysis. 2018 Mar 15;274(6):1657-1689. https://doi.org/10.1016/j.jfa.2018.01.004

Author

Elek, Gabor. / Uniformly recurrent subgroups and simple C*-algebras. In: Journal of Functional Analysis. 2018 ; Vol. 274, No. 6. pp. 1657-1689.

Bibtex

@article{1cbce5a1ff3344d2999fc3c7601019b2,
title = "Uniformly recurrent subgroups and simple C*-algebras",
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 actionadmitting 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{\textquoteright}s. We prove that if a URS is generic then its C*-algebra is simple.We give various examples of generic URS{\textquoteright}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.",
keywords = "Uniformly recurrent subgroups, Simple C⁎-algebras, Amenable traces, Graph limits",
author = "Gabor Elek",
note = "This is the author{\textquoteright}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",
year = "2018",
month = mar
day = "15",
doi = "10.1016/j.jfa.2018.01.004",
language = "English",
volume = "274",
pages = "1657--1689",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "6",

}

RIS

TY - JOUR

T1 - Uniformly recurrent subgroups and simple C*-algebras

AU - Elek, Gabor

N1 - 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

PY - 2018/3/15

Y1 - 2018/3/15

N2 - 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 actionadmitting 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.

AB - 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 actionadmitting 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.

KW - Uniformly recurrent subgroups

KW - Simple C⁎-algebras

KW - Amenable traces

KW - Graph limits

U2 - 10.1016/j.jfa.2018.01.004

DO - 10.1016/j.jfa.2018.01.004

M3 - Journal article

VL - 274

SP - 1657

EP - 1689

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 6

ER -