Galois objects and cocycle twisting for locally compact quantum groups
Abstract
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.
Keywords
Cite
@article{arxiv.0804.2405,
title = {Galois objects and cocycle twisting for locally compact quantum groups},
author = {K. De Commer},
journal= {arXiv preprint arXiv:0804.2405},
year = {2019}
}
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).