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

2012/10/01 by Mihaita Berbec, Stefaan Vaes
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Combinatorics #Countable set #Finitely-generated abelian group #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Lambda #Mathematics #Product (mathematics) #Pure mathematics #Von Neumann algebra #Von Neumann architecture #Wreath product #math.GR #math.OA

paper · pdf · doi:10.1112/plms/pdt050

published as Proceedings of the London Mathematical Society 108 (2014), 1116-1152

arxiv created 2012/10/01 · openalex publication_date 2013/09/25 · arxiv updated 2018/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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) ⋊ (Γ×Γ) is W*-superrigid. This means that the group von Neumann algebra L 𝒢 entirely remembers 𝒢. More precisely, if L 𝒢 is isomorphic with L Λ for an arbitrary countable group Λ, then Λ must be isomorphic with 𝒢.

Citations

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