Daws, M, Kasprzak, P, Skalski, A et al. (1 more author) (2012) Closed quantum subgroups of locally compact quantum groups. Advances in Mathematics, 231 (6). 3473 - 3501. ISSN 0001-8708
Abstract
We investigate the fundamental concept of a closed quantum subgroup of a locally compact quantum group. Two definitions - one due to S.Vaes and one due to S.L.Woronowicz - are analyzed and relations between them discussed. Among many reformulations we prove that the former definition can be phrased in terms of quasi-equivalence of representations of quantum groups while the latter can be related to an old definition of Podle\'s from the theory of compact quantum groups. The cases of classical groups, duals of classical groups, compact and discrete quantum groups are singled out and equivalence of the two definitions is proved in the relevant context. A deep relationship with the quantum group generalization of Herz restriction theorem from classical harmonic analysis is also established, in particular, in the course of our analysis we give a new proof of Herz restriction theorem.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | NOTICE: this is the author’s version of a work that was accepted for publication in Advances in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in Mathematics, 231 (6). 2012 http://dx.doi.org/10.1016/j.aim.2012.09.002 |
Keywords: | Herz restriction theorem; Quantum group; Quantum subgroup; Quasi-equivalence |
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: | 16 Dec 2013 11:38 |
Last Modified: | 15 Sep 2014 02:36 |
Published Version: | http://dx.doi.org/10.1016/j.aim.2012.09.002 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.aim.2012.09.002 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77164 |