Rokhlin dimension of Z^m actions on simple C*-algebras

TL;DR

This paper investigates the Rokhlin dimension of Z^m-actions on simple C*-algebras, establishing conditions for finiteness and extending previous results from automorphisms to higher-dimensional actions.

Contribution

It proves that strongly outer Z^m-actions have finite Rokhlin dimension under certain assumptions, extending known automorphism results to higher dimensions.

Findings

Strongly outer Z^m-actions have finite Rokhlin dimension.

Z^m-Bernoulli actions on infinite tensor products have finite Rokhlin dimension.

Results apply to a large class of simple C*-algebras.

Abstract

We study Rokhlin dimension of Z^m-actions on simple separable stably finite nuclear C*-algebras. We prove that under suitable assumptions, a strongly outer Z^m-action has finite Rokhlin dimension. This extends the known result for automorphisms. As an application, we show that for a large class of C*-algebras, the Z^m-Bernoulli action on the infinite tensor product has finite Rokhlin dimension.