Daws, M., Fima, P., Skalski, A. and White, S. (2016) The Haagerup property for locally compact quantum groups. Journal für die Reine und Angewandte Mathematik (Crelles Journal), 2016(711), pp. 189-229. (doi: 10.1515/crelle-2013-0113)
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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 b G; 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.
Item Type: | Articles |
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Additional Information: | MD is partially supported by EPSRC grant EP/IO26819/1. PF is partially supported by the ANR grants NEUMANN and OSQPI. AS is partially supported by the Iuventus Plus grant IP2012 043872. SW is partially supported by EPSRC grant EP/IO19227/1-2. |
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | White, Professor Stuart |
Authors: | Daws, M., Fima, P., Skalski, A., and White, S. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Journal für die Reine und Angewandte Mathematik (Crelles Journal) |
Publisher: | Walter de Gruyter |
ISSN: | 0075-4102 |
ISSN (Online): | 1435-5345 |
Copyright Holders: | Copyright © 2014 The Authors |
First Published: | First published in Journal für die Reine und Angewandte Mathematik (Crelles Journal) 2016(711):189-229 |
Publisher Policy: | Reproduced under a Creative Commons License |
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