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Classification results for nonsingular Bernoulli crossed products

Volume 268 / 2023

Stefaan Vaes, Bram Verjans 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.

Authors

  • Stefaan VaesDepartment of Mathematics
    KU Leuven
    Celestijnenlaan 200b, box 2400
    3001 Leuven, Belgium
    e-mail
  • Bram VerjansDepartment of Mathematics
    KU Leuven
    Celestijnenlaan 200b, box 2400
    3001 Leuven, Belgium
    e-mail

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