Journal of Operator Theory

Volume 66, Issue 1, Summer 2011 pp. 59-106.

Galois objects and cocycle twisting for locally compact quantum groups

Authors: Kenny De Commer
Author institution: Department of Mathematics, Universita di Tor Vergata, Roma, 00133, Italy

Summary: In this article, we investigate the notion of a Galois object for a locally compact quantum group $\mathbb{G}$. Such an object consists of a von Neumann algebra $N$, together with an ergodic integrable action of $\mathbb{G}$ on $N$ for which the crossed product is a type I factor. We show how to construct from this data a possibly different locally compact quantum group. 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: Locally compact quantum groups, Galois objects, 2-cocycles, projective representations

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