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2019 Rokhlin dimension: absorption of model actions
Gábor Szabó
Anal. PDE 12(5): 1357-1396 (2019). DOI: 10.2140/apde.2019.12.1357

Abstract

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 D is a strongly self-absorbing C-algebra and α:GA is an action on a separable, D-absorbing C-algebra that has finite Rokhlin dimension with commuting towers, then α tensorially absorbs every semi-strongly self-absorbing G-action on D. In particular, this is the case when α satisfies any version of what is called the Rokhlin property, such as for G= or G=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 k1 and on any strongly self-absorbing Kirchberg algebra, there exists a unique k-action having finite Rokhlin dimension with commuting towers up to (very strong) cocycle conjugacy.

Citation

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Gábor Szabó. "Rokhlin dimension: absorption of model actions." Anal. PDE 12 (5) 1357 - 1396, 2019. https://doi.org/10.2140/apde.2019.12.1357

Information

Received: 16 April 2018; Revised: 12 September 2018; Accepted: 18 October 2018; Published: 2019
First available in Project Euclid: 5 January 2019

zbMATH: 07006765
MathSciNet: MR3892407
Digital Object Identifier: 10.2140/apde.2019.12.1357

Subjects:
Primary: 46L55

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 5 • 2019
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