One-cohomology and the uniqueness of the group measure space decomposition of a II_1 factor

Details One-cohomology and the uniqueness of the group measure space decomposition of a II_1 factor One-cohomology and the uniqueness of the group measure space decomposition of a II_1 factor

2010-12-24

arxiv.org/abs/1012.5377v2

Mathematics

Operator Algebras

v2: minor changes, final version, to appear in Mathematische Annalen

Scientific paper

We provide a unified and self-contained treatment of several of the recent uniqueness theorems for the group measure space decomposition of a II_1 factor. We single out a large class of groups \Gamma, characterized by a one-cohomology property, and prove that for every free ergodic probability measure preserving action of \Gamma the associated II_1 factor has a unique group measure space Cartan subalgebra up to unitary conjugacy. Our methods follow closely a recent article of Chifan-Peterson, but we replace the usage of Peterson's unbounded derivations by Thomas Sinclair's dilation into a one-parameter group of automorphisms.

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