Galois objects and cocycle twisting for locally compact quantum groups

Details Galois objects and cocycle twisting for locally compact quantum groups Galois objects and cocycle twisting for locally compact quantum groups

2008-04-15

arxiv.org/abs/0804.2405v3

Mathematics

Operator Algebras

40 pages, to be published in the Journal of Operator Theory; this is a shortened version of the previous submission, whose res

Scientific paper

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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