Résume | Finite Rokhlin dimension is one of the several ways in which the Rokhlin property, a concept originally developed int the framework of amenable actions on von Neumann algebras, has been adapted to C*-dynamics. Actions with finite Rokhlin dimension have many useful features, especially in view of Elliott's classification programme. For instance, finite nuclear dimension and Z-stability are preserved when taking the crossed product of a separable unital C*-algebra by a G-action which has finite Rokhlin dimension, for a wide class of countable discrete amenable groups G.
In this talk, I'll discuss the connections of finite Rokhlin dimension with the notion of strong outerness, focusing on equivariantly Z-stable actions of residually finite, amenable, discrete, countable groups on separable, simple, unital, nuclear, Z-stable C*-algebras with non-empty trace space. In particular, I'll show that for such an action alpha on A, if the action induced by alpha on the trace space of A has small orbits in an appropriate sense, then strongly outerness is equivalent to having finite Rokhlin dimension.
The novelty of this result is the absence of topological assumption on the trace space, as opposed to past works proving analogous statements, where the trace space was always assumed to be a Bauer simplex. This is a joint work with Eusebio Gardella and Ilan Hirshberg. |