Relative C*-simplicity and characterizations for normal subgroups

Abstract

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.