The spatial Rokhlin property for actions of compact quantum groups

Barlak, S., Szabo, G. and Voigt, C. (2017) The spatial Rokhlin property for actions of compact quantum groups. Journal of Functional Analysis, 272(6), pp. 2308-2360. (doi: 10.1016/j.jfa.2016.09.023)

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Abstract

We introduce the spatial Rokhlin property for actions of coexact compact quantum groups on C∗-algebras, generalizing the Rokhlin property for both actions of classical compact groups and finite quantum groups. Two key ingredients in our approach are the concept of sequentially split ∗-homomorphisms, and the use of braided tensor products instead of ordinary tensor products. We show that various structure results carry over from the classical theory to this more general setting. In particular, we show that a number of C∗-algebraic properties relevant to the classification program pass from the underlying C∗-algebra of a Rokhlin action to both the crossed product and the fixed point algebra. Towards establishing a classification theory, we show that Rokhlin actions exhibit a rigidity property with respect to approximate unitary equivalence. Regarding duality theory, we introduce the notion of spatial approximate representability for actions of discrete quantum groups. The spatial Rokhlin property for actions of a coexact compact quantum group is shown to be dual to spatial approximate representability for actions of its dual discrete quantum group, and vice versa.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Voigt, Dr Christian
Authors: Barlak, S., Szabo, G., and Voigt, C.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Functional Analysis
Publisher:Elsevier
ISSN:0022-1236
ISSN (Online):1096-0783
Published Online:08 October 2016
Copyright Holders:Copyright © 2016 The Authors
First Published:First published in Journal of Functional Analysis 272(6):2308-2360
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
640411Quantum groups and noncommutative geometryChristian VoigtEngineering & Physical Sciences Research Council (EPSRC)EP/L013916/1M&S - MATHEMATICS