Bernoulli crossed products without almost periodic weights

Abstract

We prove a classification result for a large class of noncommutative Bernoulli crossed products $(P,\phi)^\Lambda \rtimes \Lambda$ without almost periodic states. Our results improve the classification results from [1], where only Bernoulli crossed products built with almost periodic states could be treated. We show that the family of factors $(P,\phi)^\Lambda \rtimes \Lambda$ with $P$ an amenable factor, $\phi$ a weakly mixing state (i.e. a state for which the modular automorphism group is weakly mixing) and $\Lambda$ belonging to a large class of groups, is classified by the group $\Lambda$ and the action $\Lambda \curvearrowright (P, \phi)^\Lambda$, up to state preserving conjugation of the action. [1] Stefaan Vaes and Peter Verraedt. Classification of type III Bernoulli crossed products. Adv. Math., 281:296-332, 2015.