Classification results for nonsingular Bernoulli crossed products
Volume 268 / 2023
Studia Mathematica 268 (2023), 91-120
MSC: Primary 46L36; Secondary 37A40, 46L30.
DOI: 10.4064/sm220217-11-5
Published online: 22 July 2022
Abstract
We prove rigidity and classification results for type III factors given by nonsingular Bernoulli actions of the free groups and more general free product groups. This includes a large family of nonisomorphic Bernoulli crossed products of type III$_1$ that cannot be distinguished by Connes $\tau $-invariant. These are the first such classification results beyond the well studied probability measure preserving case.
