Ozawa's class $\mathcal S$ for locally compact groups and unique prime factorization

Tobe Deprez

Ozawa's class $\mathcal S$ for locally compact groups and unique prime factorization

Operator Algebras 2019-04-29 v2 Dynamical Systems Group Theory

Authors: Tobe Deprez

Abstract

We study class $\mathcal S$ for locally compact groups. We characterize locally compact groups in this class as groups having an amenable action on a boundary that is small at infinity, generalizing a theorem of Ozawa. Using this characterization, we provide new examples of groups in class $\mathcal S$ and prove unique prime factorization results for group von Neumann algebras of products of locally compact groups in this class. We also prove that class $\mathcal S$ is a measure equivalence invariant.

Keywords

group actions von neumann algebras

Cite

@article{arxiv.1904.02090,
  title  = {Ozawa's class $\mathcal S$ for locally compact groups and unique prime factorization},
  author = {Tobe Deprez},
  journal= {arXiv preprint arXiv:1904.02090},
  year   = {2019}
}

Comments

v2: changed references to and comments on examples at the end of introduction; more general version of Proposition 4.4

Ozawa's class $\mathcal S$ for locally compact groups and unique prime factorization

Abstract

Keywords

Cite

Comments

Related papers