Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups

International audienceWe 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