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An intrinsic characterization of C*-simplicity

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arxiv 1509.01870 v5 pith:UBG6M3MS submitted 2015-09-07 math.OA math.GR

Matthew Kennedy This is my paper · ORCID
classification math.OAmath.GR
keywords simplegroupcharacterizationintrinsiconlypropertyprovealgebra
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A group is said to be C*-simple if its reduced C*-algebra is simple. We establish an intrinsic (group-theoretic) characterization of groups with this property. Specifically, we prove that a discrete group is C*-simple if and only if it has no non-trivial amenable uniformly recurrent subgroups. We further prove that a group is C*-simple if and only if it satisfies an averaging property considered by Powers.

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  1. A Groupoid Picture of Elek Algebras

    math.OA 2019-08 accept novelty 6.0 of 10

    A new groupoid model for Elek's C*-algebras is constructed, and the C*-algebra is shown to be nuclear exactly when the associated Schreier graph has local property A.

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