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

By Mihaita Berbec, S. Vaes. 2012

53 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1dcb164cede59a34aa6e2c7fb43b0c01056b970c

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In Algebra and Number Theory

1. Adrian Ioana
2. S. Vaes
3. Sorin Popa
4. Mihaita Berbec
5. J. Peterson

In Geometry and Topology

1. Adrian Ioana
2. S. Vaes
3. Sorin Popa
4. J. Peterson
5. Damien Gaboriau
6. Thomas Sinclair
7. A. Furman

In Mathematical Physics

1. Adrian Ioana
2. S. Vaes
3. Sorin Popa
4. Mihaita Berbec
5. J. Peterson
6. Thomas Sinclair
7. Damien Gaboriau
8. A. Furman

Citations in the corpus

• RIGIDITY FOR VON NEUMANN ALGEBRAS (2017, background): “ (in fact, unitarily conjugate modulo scalars inside M) from the mere existence of u. Following [IPV10], several other classes of W∗-superrigid groups were found in [BV12,CI17]. Thus, it was shown in [BV12] that the left-right wreath product Γ = (Z/2Z)(Γ) ⋊(Γ×Γ) is W∗-superrigid, for any icc hyperbo”