Daws, M (2016) Categorical aspects of quantum groups: multipliers and intrinsic groups. Canadian Journal of Mathematics, 68 (2). pp. 309-333. ISSN 0008-414X
Abstract
We show that the assignment of the (left) completely bounded multiplier algebra M(l)cb¹(G))to a locally compact quantum group (G), and the assignment of the intrinsic group, form functors between appropriate categories. Morphisms of locally compact quantum groups can be described by Hopf *-homomorphisms between universal C*-algebras, by bicharacters, or by special sorts of coactions. We show that the whole theory of completely bounded multipliers can be lifted to the universal C*-algebra level, and that then the different pictures of both multipliers (reduced, universal, and as centralisers) and morphisms interact in extremely natural ways. The intrinsic group of a quantum group can be realised as a class of multipliers, and so our techniques immediately apply. We also show how to think of the intrinsic group using the universal C*-algebra picture, and then, again, show how the differing views on the intrinsic group interact naturally with morphisms. We show that the intrinsic group is the "maximal classical" quantum subgroup of a locally compact quantum group, show that it is even closed in the strong Vaes sense, and that the intrinsic group functor is an adjoint to the inclusion functor from locally compact groups to quantum groups.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Canadian Mathematical Society 2016. This is an author produced version of a paper published in Canadian Journal of Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | locally compact quantum group, morphism, intrinsic group, multiplier, centraliser |
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: | 27 Mar 2015 10:58 |
Last Modified: | 13 Dec 2016 02:01 |
Published Version: | https://doi.org/10.4153/CJM-2015-022-0 |
Status: | Published |
Publisher: | Canadian Mathematical Society |
Identification Number: | 10.4153/CJM-2015-022-0 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:83381 |