Vol. 12, No. 5, 2019

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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-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 : G A 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 k 1 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.

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Keywords
Rokhlin dimension, C*-dynamical system, strongly self-absorbing C*-algebra
Mathematical Subject Classification 2010
Primary: 46L55
Milestones
Received: 16 April 2018
Revised: 12 September 2018
Accepted: 18 October 2018
Published: 15 December 2018
Authors
Gábor Szabó
Department of Mathematics
KU Leuven
Leuven
Belgium