Unique Cartan decomposition for II_1 factors arising from arbitrary actions of hyperbolic groups

Details Unique Cartan decomposition for II_1 factors arising from arbitrary actions of hyperbolic groups Unique Cartan decomposition for II_1 factors arising from arbitrary actions of hyperbolic groups

2012-01-12

arxiv.org/abs/1201.2824v3

Mathematics

Operator Algebras

v3: Considerably simplified proof of the main result. v2: Improved exposition; new result proving uniqueness of Cartan for cro

Scientific paper

We prove that for any free ergodic probability measure preserving action
$\Gamma \actson (X,\mu)$ of a non-elementary hyperbolic group, or a lattice in
a rank one simple Lie group, the associated group measure space II_1 factor
$L^\infty(X) \rtimes \Gamma$ has L^\infty(X) as its unique Cartan subalgebra,
up to unitary conjugacy.

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