Rokhlin dimension: absorption of model actions

Abstract

In this paper, we establish a connection between Rokhlin dimension and the absorption of certain model actions on strongly self-absorbing C*-algebras. Namely, as to be made precise in the paper, let $G$ be a well-behaved locally compact group. If $\mathcal{D}$ is a strongly self-absorbing C*-algebra, and $\alpha :G\curvearrowright A$ is an action on a separable, $\mathcal{D}$-absorbing C*-algebra that has finite Rokhlin dimension with commuting towers, then $\alpha$ tensorially absorbs every semi-strongly self-absorbing $G$-actions on $\mathcal{D}$. 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 non-trivial applications. Most notably it is shown that for any $k\ge 1$ and on any strongly self-absorbing Kirchberg algebra, there exists a unique ${\mathbb{R}}^k$-action having finite Rokhlin dimension with commuting towers up to (very strong) cocycle conjugacy.

v2 40 pages; this version has been accepted for publication in Analysis & PDE

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Cited by in corpus (4)

• Equivariant property (SI) revisited
• On a categorical framework for classifying C*-dynamics up to cocycle conjugacy
• Actions of certain torsion-free elementary amenable groups on strongly self-absorbing C*-algebras
• Equivariant bundles and absorption