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arXiv · 1210.0336

W*-superrigidity for group von Neumann algebras of left-right wreath products

Mihaita Berbec·Stefaan Vaes
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Abstract

We prove that for many nonamenable groups Γ, including all hyperbolic groups and all nontrivial free products, the left-right wreath product group G := (Z/2Z)^(Γ) \rtimes (Γ\times Γ) is W*-superrigid. This means that the group von Neumann algebra LG entirely remembers G. More precisely, if LG is isomorphic with LΛfor an arbitrary countable group Λ, then Λmust be isomorphic with G.

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Mihaita Berbec, Stefaan Vaes. 2012-10-01. W*-superrigidity for group von Neumann algebras of left-right wreath products. https://doi.org/10.1112/plms%2Fpdt050

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