A Rokhlin type theorem for simple C*-algebras of finite nuclear dimension

TL;DR

This paper proves that certain Z-actions on simple, finite nuclear dimension C*-algebras have finite Rokhlin dimension under specific conditions, advancing the understanding of symmetries in operator algebras.

Contribution

It establishes a Rokhlin type theorem for Z-actions on simple C*-algebras with finite nuclear dimension, under trace space conditions.

Findings

Strongly outer Z-actions have finite Rokhlin dimension.

The result applies when the trace space has a compact, finite-dimensional extreme boundary.

The action on the trace space is assumed to be trivial.

Abstract

We study Z-actions on unital simple separable stably finite C*-algebras of finite nuclear dimension. Assuming that the extreme boundary of the trace space is compact and finite dimensional, and that the induced action on the trace space is trivial, we show that strongly outer Z-actions have finite Rokhlin dimension in the sense of Hirshberg, Winter and Zacharias.