Factoriality of twisted locally compact group von Neumann algebras

Abstract

In this short note, we construct an exotic example of a locally compact group $G$ with a Borel $2$-cocycle $\omega$ such that the non-twisted group von Neumann algebra $L(G)$ is a factor, while the twisted group von Neumann algebra $L_{\omega }(G)$ has a diffuse center.

v3: minor corrections, final version, to appear in Comptes Rendus Mathématique de l'Académie des Sciences Paris

References in corpus (1)

• Braided tensor product of von Neumann algebras