| Résume | An action of a countable group on a C* -algebra is called equivariantly Z-stable if it tensorially absorbs the trivial action on the Jiang-Su algebra. Analogous to ordinary Z-stability, equivariant Z-stability is an important regularity property in the context of the classification of amenable group actions on classifiable C* -algebras. In this talk I will explain the relevance and nature of this property and discuss for which actions positive results were already obtained establishing the property. In particular, I will present my own recent result: I have proved that the property holds automatically for all automorphisms on algebraically simple, separable, nuclear, Z-stable C* -algebras for which the trace space is a Bauer simplex with finite-dimensional extremal boundary. At least for automorphisms this is a generalization of a previous result by Gardella-Hirshberg-Vaccaro. |
