Crossed-products by locally compact groups: Intermediate subfactors

Abstract

We study actions of locally compact groups on von Neumann factors and the associated crossed-product von Neumann algebras. In the setting of totally disconnected groups we provide sufficient conditions on an action $G\curvearrowright Q$ ensuring that the inclusion $Q\subset Q⋊G$ is irreducible and that every intermediate subfactor is of the form $Q⋊H$ for a closed subgroup $H<G$. This partially generalizes a result of Izumi-Longo-Popa [ILP98] and Choda [Ch78]. We moreover show that one can not hope to use their strategy for non-discrete groups.

29 pages

References in corpus (1)

• Crossed products by Hecke pairs I: *-algebraic theory