arXiv 0804.24052008-04math.OAmath.QA

Galois objects and cocycle twisting for locally compact quantum groups

K. De Commer

备注：: 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).
发表信息：: Journal of Operator Theory, 66 (1) (2011) 59-106

英文摘要：

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.

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