Bernoulli Crossed Products Without Almost Periodic Weights

Abstract

We prove a classification result for a large class of noncommutative Bernoulli crossed products (P, φ) Λ ⋊ Λ without almost periodic states. Our results improve the classification results from [VV14], where only Bernoulli crossed products built with almost periodic states could be treated. We show that the family of factors (P, φ) Λ ⋊ Λ with P an amenable factor, φ a weakly mixing state (i.e. a state for which the modular automorphism group is weakly mixing) and Λ belonging to a large class of groups, is classified by the group Λ and the action Λ (P, φ) Λ , up to state preserving conjugation of the action.

Unitary conjugacy for type III subfactors and W$^*$-superrigidity

“…The Bernoulli action in this theorem was intensively studied in [VV14,Ve15]. They obtained similar conclusions if the action Λ β (A, ψ) is also a Bernoulli action of a group in the class C. Now thanks to our Theorem C, we can put arbitrary actions as Λ β (A, ψ).…”