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arXiv · 2010.01223

New examples of W$^*$ and C$^*$-superrigid groups

Ionut Chifan·Alec Diaz-Arias·Daniel Drimbe
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Abstract

A group $G$ is called $W^*$-superrigid (resp. $C^*$-superrigid) if it is completely recognizable from its von Neumann algebra $L(G)$ (resp. reduced $C^*$-algebra $C_r^*(G)$). Developing new technical aspects in Popa's deformation/rigidity theory we introduce several new classes of $W^*$-superrigid groups which appear as direct products, semidirect products with non-amenable core and iterations of amalgamated free products and HNN-extensions. As a byproduct we obtain new rigidity results in $C^*$-algebra theory including additional examples of $C^*$-superrigid groups and explicit computations of symmetries of reduced group $C^*$-algebras.

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Ionut Chifan, Alec Diaz-Arias, Daniel Drimbe. 2020-10-02. New examples of W$^*$ and C$^*$-superrigid groups. https://arxiv.org/abs/2010.01223

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