Rokhlin dimension and C*-dynamics

Hirshberg, I., Winter, W. and Zacharias, J. (2015) Rokhlin dimension and C*-dynamics. Communications in Mathematical Physics, 335(2), pp. 637-670. (doi:10.1007/s00220-014-2264-x)

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Abstract

We develop the concept of Rokhlin dimension for integer and for finite group actions on C∗-algebras. Our notion generalizes the so-called Rokhlin property, which can be thought of as Rokhlin dimension 0. We show that finite Rokhlin dimension is prevalent and appears in cases in which the Rokhlin property cannot be expected: the property of having finite Rokhlin dimension is generic for automorphisms of Z-stable C∗-algebras, where Z denotes the Jiang–Su algebra. Moreover, crossed products by automorphisms with finite Rokhlin dimension preserve the property of having finite nuclear dimension, and under a mild additional hypothesis also preserve Z-stability. In topological dynamics our notion may be interpreted as a topological version of the classical Rokhlin lemma: automorphisms arising from minimal homeomorphisms of finite dimensional compact metrizable spaces always have finite Rokhlin dimension. The latter result has by now been generalized by Szabó to the case of free and aperiodic Zd -actions on compact metrizable and finite dimensional spaces.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Zacharias, Dr Joachim
Authors: Hirshberg, I., Winter, W., and Zacharias, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Communications in Mathematical Physics
Publisher:Springer Berlin Heidelberg
ISSN:0010-3616
ISSN (Online):1432-0916
Copyright Holders:Copyright © 2015 The Authors
First Published:First published in Communications in Mathematical Physics 335(2):637-670
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
626331The Cuntz Semigroup and the Fine Stucture of Nuclear C*-AlgebrasJoachim ZachariasEngineering & Physical Sciences Research Council (EPSRC)EP/I019227/1M&S - MATHEMATICS