Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups

Rémi Boutonnet; Alessandro Carderi

Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups

Operator Algebras 2015-04-28 v2 Group Theory

Authors: Rémi Boutonnet , Alessandro Carderi

Abstract

We prove that for any infinite, maximal amenable subgroup $H$ in a hyperbolic group $G$ , the von Neumann subalgebra $LH$ is maximal amenable inside $LG$ . It provides many new, explicit examples of maximal amenable subalgebras in II $_1$ factors. We also prove similar maximal amenability results for direct products of relatively hyperbolic groups and orbit equivalence relations arising from measure-preserving actions of such groups.

Keywords

von Neumann algebras maximal amenable subalgebras hyperbolic groups II$_1$ factors orbit equivalence relations measure-preserving actions

Cite

@article{arxiv.1310.5864,
  title  = {Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups},
  author = {Rémi Boutonnet and Alessandro Carderi},
  journal= {arXiv preprint arXiv:1310.5864},
  year   = {2015}
}

Comments

16 pages, 2 figures, new section added about direct products. Accepted for publication to Mathematische Annalen

Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups

Abstract

Keywords

Cite

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