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arXiv:0804.2405 [math.OA]AbstractReferencesReviewsResources

Galois objects and cocycle twisting for locally compact quantum groups

K. De Commer

Published 2008-04-15, updated 2010-03-31Version 3

In this article, we investigate the notion of a Galois object for a locally compact quantum group M. Such an object consists of a von Neumann algebra N equipped with an ergodic integrable coaction of M on N, such that the crossed product is a type I factor. We show how to construct from such a coaction a new locally compact quantum group P, which we call the reflection of M along N. By way of application, we prove the following statement: any twisting of a locally compact quantum group by a unitary 2-cocycle is again a locally compact quantum group.

Comments: 40 pages, to be published in the Journal of Operator Theory; this is a shortened version of the previous submission, whose results have been subsumed in our PhD thesis (available at http://hdl.handle.net/1979/2662).
Journal: Comm. Math. Phys. 304 (1) (2011), 187-228
Categories: math.OA, math.QA
Subjects: 46L65
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