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- W2797641848 abstract "We show that any infinite collection $(Gamma_n)_{nin mathbb N}$ of icc, hyperbolic, property (T) groups satisfies the following von Neumann algebraic emph{infinite product rigidity} phenomenon. If $Lambda$ is an arbitrary group such that $L(oplus_{nin mathbb N} Gamma_n)cong L(Lambda)$ then there exists an infinite direct sum decomposition $Lambda=(oplus_{n in mathbb N} Lambda_n )oplus A$ with $A$ icc amenable such that, for all $nin mathbb N$, up to amplifications, we have $L(Gamma_n) cong L(Lambda_n)$ and $L(oplus_{kgeq n} Gamma_k )cong L((oplus_{kgeq n} Lambda_k) oplus A)$. The result is sharp and complements the previous finite product rigidity property found in [CdSS16]. Using this we provide an uncountable family of restricted wreath products $GammacongSigmawr Delta$ of icc, property (T) groups $Sigma$, $Delta$ whose wreath product structure is recognizable, up to a normal amenable subgroup, from their von Neumann algebras $L(Gamma)$. Along the way we highlight several applications of these results to the study of rigidity in the $mathbb C^*$-algebra setting." @default.
- W2797641848 created "2018-04-24" @default.
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- W2797641848 date "2018-04-12" @default.
- W2797641848 modified "2023-09-27" @default.
- W2797641848 title "Some rigidity results for II$_1$ factors arising from wreath products of property (T) groups." @default.
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