Journal of Operator Theory

Volume 87, Issue 2, Spring 2022 pp. 471-486.

Relative $C^*$-simplicity and characterizations for normal subgroups

Authors: Dan Ursu
Author institution: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Summary: The notion of a plump subgroup was recently introduced by Amrutam. This is a relativized version of Powers' averaging property, and it is known that Powers' averaging property is equivalent to $C^*$-simplicity. With this in mind, we introduce a relativized notion of $C^*$-simplicity, and show that for normal subgroups it is equivalent to plumpness, along with several other characterizations.

DOI: http://dx.doi.org/10.7900/jot.2020oct26.2293
Keywords: group action, Furstenberg boundary, reduced $C^*$-algebra, crossed product, simplicity

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