#### Vol. 12, No. 5, 2019

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
Rokhlin dimension: absorption of model actions

### Gábor Szabó

Vol. 12 (2019), No. 5, 1357–1396
##### Abstract

We establish a connection between Rokhlin dimension and the absorption of certain model actions on strongly self-absorbing ${C}^{\ast }$-algebras. Namely, as to be made precise in the paper, let $G$ be a well-behaved locally compact group. If $\mathsc{D}$ is a strongly self-absorbing ${C}^{\ast }$-algebra and $\alpha :G↷A$ is an action on a separable, $\mathsc{D}$-absorbing ${C}^{\ast }$-algebra that has finite Rokhlin dimension with commuting towers, then $\alpha$ tensorially absorbs every semi-strongly self-absorbing $G$-action on $\mathsc{D}$. In particular, this is the case when $\alpha$ satisfies any version of what is called the Rokhlin property, such as for $G=ℝ$ or $G={ℤ}^{k}$. This contains several existing results of similar nature as special cases. We will in fact prove a more general version of this theorem, which is intended for use in subsequent work. We will then discuss some nontrivial applications. Most notably it is shown that for any $k\ge 1$ and on any strongly self-absorbing Kirchberg algebra, there exists a unique ${ℝ}^{k}$-action having finite Rokhlin dimension with commuting towers up to (very strong) cocycle conjugacy.

##### Keywords
Rokhlin dimension, C*-dynamical system, strongly self-absorbing C*-algebra
Primary: 46L55