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arXiv · 1010.5077

A class of groups for which every action is W*-superrigid

Cyril Houdayer·Sorin Popa·Stefaan Vaes
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Abstract

We prove the uniqueness of the group measure space Cartan subalgebra in crossed products A \rtimes Γcovering certain cases where Γis an amalgamated free product over a non-amenable subgroup. In combination with Kida's work we deduce that if Σ< SL(3,\Z) denotes the subgroup of matrices g with g_31 = g_32 = 0, then any free ergodic probability measure preserving action of Γ= SL(3,\Z) *_ΣSL(3,\Z) is stably W*-superrigid. In the second part we settle a technical issue about the unitary conjugacy of group measure space Cartan subalgebras.

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Cyril Houdayer, Sorin Popa, Stefaan Vaes. 2011-10-20. A class of groups for which every action is W*-superrigid. https://arxiv.org/abs/1010.5077

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