Daws, M (2010) A Note on Operator biprojectivity of compact quantum groups. Proceedings of the American Mathematical Society, 138 (4). 1349 - 1359. ISSN 0002-9939
Abstract
Given a (reduced) locally compact quantum group A, we can consider the convolution algebra L1(A) (which can be identified as the predual of the von Neumann algebra form of A). It is conjectured that L1(A) is operator biprojective if and only if A is compact. The "only if" part always holds, and the "if" part holds for Kac algebras. We show that if the splitting morphism associated with L1(A) being biprojective can be chosen to be completely positive,or just contractive, then we already have a Kac algebra. We give another proof of the converse, indicating how modular properties of the Haar state seem to be important.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2010, American Mathematical Society. This is an author produced version of a paper published in the Proceedings of the American Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. First published in the Proceedings of the American Mathematical Society in volume 138, issue 4, 2010, published by the American Mathematical Society. |
Keywords: | Compact quantum group; Biprojective; Kac algebra; Modular automorphism 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: | 16 Dec 2013 12:23 |
Last Modified: | 15 Sep 2014 02:37 |
Published Version: | http://dx.doi.org/10.1090/S0002-9939-09-10220-4 |
Status: | Published |
Publisher: | American Mathematical Society |
Identification Number: | 10.1090/S0002-9939-09-10220-4 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77167 |