Daws, M and Le Pham, H (2013) Isometries between quantum convolution algebras. Quarterly Journal of Mathematics, 64 (2). 373 - 396. ISSN 0033-5606
Abstract
Given locally compact quantum groups G and G, we show that if the convolution algebras L(G) and L (G) are isometrically isomorphic as algebras, then G is isomorphic either to G or to the commutant G ′. Furthermore, given an isometric algebra isomorphism θ:L(G)→L(G), the adjoint is a *-isomorphism between L(G) and either L(G) or its commutant, composed with a twist given by a member of the intrinsic group of L(G ). This extends known results for Kac algebras (although our proofs are somewhat different), which in turn generalized classical results of Wendel and Walter. We show that the same result holds for isometric algebra homomorphisms between quantum measure algebras (either reduced or universal). We make some remarks about the intrinsic groups of the enveloping von Neumann algebras of C*-algebraic quantum groups.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is a pre-copyedited, author-produced PDF of an article accepted for publication in the Quarterly Journal of Mathematics following peer review. The definitive publisher-authenticated version Daws, M and Le Pham, H (2013) Isometries between quantum convolution algebras. Quarterly Journal of Mathematics, 64 (2). 373 - 396. ISSN 0033-5606 is available online at: http://dx.doi.org/10.1093/qmath/has008 |
Keywords: | Locally compact quantum group; Isometric isomor phism; Intrinsic group |
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: | 17 Dec 2013 11:46 |
Last Modified: | 15 Sep 2014 02:36 |
Published Version: | http://dx.doi.org/10.1093/qmath/has008 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/qmath/has008 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77172 |