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.
An intrinsic characterization of C*-simplicity
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abstract
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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2019 1verdicts
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A Groupoid Picture of Elek Algebras
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.