Crossed products of von Neumann algebras and semi-direct products of groups

Abstract

Starting from a W ∗-covariant system ( M, β, A × α G) we construct a new covariant system, where the locally compact group is G but where the von Neumann algebra itself is a crossed product. We show that the crossed products associated with those two covariant systems are spatially isomorphic. We further give some deeper insight in this result by relating it to a general theorem on induction in stages.