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- W2620491499 abstract "We provide a fairly large family of amalgamated free product groups $Gamma=Gamma_1ast_{Sigma}Gamma_2$ whose amalgam structure can be completely recognized from their von Neumann algebras. Specifically, assume that $Gamma_i$ is a product of two icc non-amenable bi-exact (e.g., hyperbolic) groups, and $Sigma$ is icc amenable and has trivial one-sided commensurator in $Gamma_i$, for every $iin{1,2}$. Then $Gamma$ satisfies the following rigidity property: any group $La$ such that $L(La)$ is isomorphic to $L(G)$ admits an amalgamated free product decomposition $La=La_1ast_Delta La_2$ such that the inclusions $L(Delta)subseteq L(La_i)$ and $L(Sigma)subseteq L(G_i)$ are isomorphic, for every $iin{1,2}$. This result significantly strengthens some of the previous Bass-Serre rigidity results for von Neumann algebras. As a corollary, we obtain the first examples of amalgamated free product groups which are W$^*$-superrigid." @default.
- W2620491499 created "2017-06-05" @default.
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- W2620491499 date "2017-05-20" @default.
- W2620491499 modified "2023-09-27" @default.
- W2620491499 title "Amalgamated Free Product Rigidity for Group von Neumann Algebras" @default.
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