Compact quantum metric spaces from quantum groups of rapid decay

Bhowmick, J., Voigt, C. and Zacharias, J. (2015) Compact quantum metric spaces from quantum groups of rapid decay. Journal of Noncommutative Geometry, 9(4), pp. 1175-1200. (doi:10.4171/JNCG/220)

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Abstract

We present a modified version of the definition of property RD for discrete quantum groups given by Vergnioux in order to accommodate examples of non-unimodular quantum groups. Moreover we extend the construction of spectral triples associated to discrete groups with length functions, originally due to Connes, to the setting of quantum groups. For quantum groups of rapid decay we study the resulting spectral triples from the point of view of compact quantum metric spaces in the sense of Rieffel.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Voigt, Dr Christian and Zacharias, Dr Joachim
Authors: Bhowmick, J., Voigt, C., and Zacharias, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Noncommutative Geometry
Publisher:European Mathematical Society
ISSN:1661-6952
ISSN (Online):1661-6960
Copyright Holders:Copyright © 2014 European Mathematical Society
First Published:First published in Journal of Noncommutative Geometry 2015
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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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
596411The Cuntz Semigroup and the Fine Structure of Nuclear C*-AlgebrasStuart WhiteEngineering & Physical Sciences Research Council (EPSRC)EP/I019227/1M&S - MATHEMATICS