English

Galois objects and cocycle twisting for locally compact quantum groups

Operator Algebras 2019-01-29 v3 Quantum Algebra

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).

R2 v1 2026-06-21T10:31:08.234Z