Daws, M orcid.org/0000-0003-1707-4308, Fima, P, Skalski, A et al. (1 more author) (2016) The Haagerup property for locally compact quantum groups. Journal für die reine und angewandte Mathematik, 2016 (711). pp. 189-229. ISSN 0075-4102
Abstract
The Haagerup property for locally compact groups is generalised to the context of locally compact quantum groups, with several equivalent characterisations in terms of the unitary representations and positive-definite functions established. In particular it is shown that a locally compact quantum group [G] has the Haagerup property if and only if its mixing representations are dense in the space of all unitary representations. For discrete [G] we characterise the Haagerup property by the existence of a symmetric proper conditionally negative functional on the dual quantum group [Gˆ]; by the existence of a real proper cocycle on [G], and further, if [G] is also unimodular we show that the Haagerup property is a von Neumann property of [G]. This extends results of Akemann, Walter, Bekka, Cherix, Valette, and Jolissaint to the quantum setting and provides a connection to the recent work of Brannan. We use these characterisations to show that the Haagerup property is preserved under free products of discrete quantum groups.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | math.OA; math.OA; math.QA |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Mar 2014 12:24 |
Last Modified: | 08 Apr 2021 15:12 |
Status: | Published |
Publisher: | De Gruyter |
Identification Number: | 10.1515/crelle-2013-0113 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77163 |