W$^*$-superrigidity for wreath products with groups having positive first $\ell^2$-Betti number

Mihaita Berbec

W$^*$-superrigidity for wreath products with groups having positive first $\ell^2$-Betti number

Operator Algebras 2014-12-12 v2 Group Theory

Authors: Mihaita Berbec

Abstract

In [BV12] we have proven that, for all hyperbolic groups and for all non-trivial free products $\Gamma$ , the left-right wreath product group $G:=(Z/2Z)^{(\Gamma)} \rtimes (\Gamma \times \Gamma)$ is W $^*$ -superrigid. In this paper, we extend this result to other classes of countable groups. More precisely, we prove that for weakly amenable groups $\Gamma$ having positive first $\ell^2$ -Betti number, the same wreath product $G$ is W $^*$ -superrigid.

Keywords

W$^*$-superrigidity wreath products $\ell^2$-Betti number weakly amenable groups von Neumann algebras countable groups

Cite

@article{arxiv.1403.7110,
  title  = {W$^*$-superrigidity for wreath products with groups having positive first $\ell^2$-Betti number},
  author = {Mihaita Berbec},
  journal= {arXiv preprint arXiv:1403.7110},
  year   = {2014}
}

Comments

v2: minor changes, to appear in Int. J. Math

W$^*$-superrigidity for wreath products with groups having positive first $\ell^2$-Betti number

Abstract

Keywords

Cite

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