Equivariant uniform property Gamma and Z-stability

Lise Wouters (KU Leuven)

Thursday 20th October, 2022 16:00-17:00 Maths 311B


In this talk, I will discuss equivariant uniform property Gamma for group actions on C*-algebras. Recently, Gábor Szabó and I have been able to show that for actions of countable amenable groups on unital, separable C*-algebras this property (roughly speaking) allows one to deduce uniform tracial information about the action from information about several equivariant tracial representations separately. This is the dynamical analogue of a result of Castillejos-Evington-Tikuisis-White-Winter, and generalizes a previous result of this type by Gardella-Hirshberg-Vaccaro. I will explain our result and how this leads to an important application: all actions of countable amenable groups on unital, simple, separable, nuclear, Z-stable C*-algebras with equivariant property Gamma are automatically equivariantly Z-stable.

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