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arXiv · 1012.5377

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

Stefaan Vaes
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Abstract

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 Γ, characterized by a one-cohomology property, and prove that for every free ergodic probability measure preserving action of Γthe 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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Stefaan Vaes. 2012-02-10. One-cohomology and the uniqueness of the group measure space decomposition of a II_1 factor. https://arxiv.org/abs/1012.5377

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