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

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.

References in corpus (4)

• On a Class of Type II${}_1$ Factors with Betti Numbers Invariants
• Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)
• On a class of ${\mathrm{II}}_1$ factors with at most one Cartan subalgebra
• On co-amenability for groups and von Neumann algebras

Cited by in corpus (15)

• Structure of $\mathrm{I}{\mathrm{I}}_1$ factors arising from free Bogoljubov actions of arbitrary groups
• W${}^{\ast }$-Rigidity for the von Neumann Algebras of Products of Hyperbolic Groups
• Primeness results for von Neumann algebras associated with surface braid groups
• Some Applications of Group Theoretic Rips Constructions to the Classification of von Neumann Algebras
• Orbit equivalence rigidity for product actions
• Von Neumann equivalence and properly proximal groups
• Prime II${}_1$ factors arising from irreducible lattices in products of rank one simple Lie groups
• Product rigidity in von Neumann and C${}^{\ast }$-algebras via s-malleable deformations
• Free nilpotent groups are C*-superrigid
• W*-superrigidity for groups with infinite center
• W*-superrigidity for cocycle twisted group von Neumann algebras
• Wreath-like products of groups and their von Neumann algebras I: $W^{\ast }$-superrigidity
• Strong primeness for equivalence relations arising from Zariski dense subgroups
• W${}^{\ast }$-superrigidity for wreath products with groups having positive first ${\ell }^2$-Betti number
• W*-superrigidity for discrete quantum groups