Daws, M orcid.org/0000-0003-1707-4308, Skalski, A and Viselter, A (2017) Around Property (T) for Quantum Groups. Communications in Mathematical Physics, 353 (1). pp. 69-118. ISSN 0010-3616
Abstract
We study Property (T) for locally compact quantum groups, providing several new characterisations, especially related to operator algebraic ergodic theory. Quantum Property (T) is described in terms of the existence of various Kazhdan type pairs, and some earlier structural results of Kyed, Chen and Ng are strengthened and generalised. For second countable discrete unimodular quantum groups with low duals, Property (T) is shown to be equivalent to Property (T)1,1 of Bekka and Valette. This is used to extend to this class of quantum groups classical theorems on ‘typical’ representations (due to Kerr and Pichot), and on connections of Property (T) with spectral gaps (due to Li and Ng) and with strong ergodicity of weakly mixing actions on a particular von Neumann algebra (due to Connes and Weiss). Finally, we discuss in the Appendix equivalent characterisations of the notion of a quantum group morphism with dense image.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © The Author(s) 2017 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Environment (Leeds) > School of Geography (Leeds) > Centre for Spatial Analysis & Policy (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 15 Nov 2017 15:09 |
Last Modified: | 23 Jun 2023 22:39 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00220-017-2862-5 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:124081 |