Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Operator biprojectivity of compact quantum groups

Author(s): Matthew Daws
Journal: Proc. Amer. Math. Soc. 138 (2010), 1349-1359.
MSC (2010): Primary 46L89, 46M10; Secondary 22D25, 46L07, 46L65, 47L25, 47L50, 81R15
Posted: November 25, 2009
MathSciNet review: 2578527
Retrieve article in: PDF

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Abstract: Given a (reduced) locally compact quantum group , we can consider the convolution algebra (which can be identified as the predual of the von Neumann algebra form of ). It is conjectured that is operator biprojective if and only if 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 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.

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