Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups

@article{Boutonnet2013MaximalAS,
  title={Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups},
  author={R'emi Boutonnet and Alessandro Carderi},
  journal={Mathematische Annalen},
  year={2013},
  volume={367},
  pages={1199-1216}
}
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$$_1$$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. 
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