W*-superrigidity for wreath products with groups having positive first ℓ2-Betti number
W*-superrigidity for wreath products with groups having positive first ℓ2-Betti number
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W*-第一个 ℓ2-Betti 数为正数的花环产品的超刚性
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发表时间：
2014
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通讯作者：
Mihaita Berbec
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作者：
Mihaita Berbec
在[M. Berbec和S. Vaes，W*-superrigidity for group von Neumann algebras of left-right wreath products，Proc.伦敦Math.Soc.108（2014）1116-1152]我们已经证明了，对于所有双曲群和所有非平凡自由积Γ，左-右环积群？<$（<$/2 <$）（Γ）<$（Γ × Γ）是W*-超刚性的，在这个意义下，它的群von Neumann代数L？完全记得那群人？本文将这一结果推广到其它可数群类。更确切地说，我们证明了弱顺从群Γ具有积极的第一l2-Betti数，相同的圈积群？是W*-超刚性
In [M. Berbec and S. Vaes, W*-superrigidity for group von Neumann algebras of left–right wreath products, Proc. London Math. Soc.108 (2014) 1116–1152] we have proven that, for all hyperbolic groups and for all nontrivial free products Γ, the left–right wreath product group ? ≔ (ℤ/2ℤ)(Γ) ⋊ (Γ × Γ) is W*-superrigid, in the sense that its group von Neumann algebra L? completely remembers the group ?. In this paper, we extend this result to other classes of countable groups. More precisely, we prove that for weakly amenable groups Γ having positive first l2-Betti number, the same wreath product group ? is W*-superrigid.