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One-cohomology and the uniqueness of the group measure space decomposition of a II1 factor

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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 II1 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 Γ the associated II1 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 malleable deformation by a one-parameter group of automorphisms.

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Authors and Affiliations

  1. KU Leuven, Celestijnenlaan 200B, 3001, Leuven, Belgium

    Stefaan Vaes

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  1. Stefaan Vaes
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Correspondence to Stefaan Vaes.

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Partially supported by ERC Starting Grant VNALG-200749, Research Programme G.0639.11 of the Research Foundation—Flanders (FWO) and K.U.Leuven BOF research grant OT/08/032.

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Vaes, S. One-cohomology and the uniqueness of the group measure space decomposition of a II1 factor. Math. Ann. 355, 661–696 (2013). https://doi.org/10.1007/s00208-012-0797-x

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  • DOI: https://doi.org/10.1007/s00208-012-0797-x

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