论文标题
Von Neumann和C $^*$ - 代数的产品刚度通过S损坏变形
Product rigidity in von Neumann and C$^*$-algebras via s-malleable deformations
论文作者
论文摘要
我们提供了一类新的可数级别ICC组$ \ MATHCAL a $，该产品的刚度是[CDSS15]所产生的：如果$γ_1，\ dots，γ_n\ in \ Mathcal a $ a $ and $λ$是$ l（γ_1\ times \ times \ times \ times \ times \timesγ_n）$ comp and progmant progant possity progn（comm） $λ=λ_1\ times \ dots \ timesλ_n$，以至于$ l（λ_i）$稳定在$ l（γ_i）$上，对于任何$ 1 \ leq i \ leq n $。 Class $\mathcal A$ consists of groups $Γ$ for which $L(Γ)$ admits an s-malleable deformation in the sense of Sorin Popa and it includes all non-amenable groups $Γ$ such that either (a) $Γ$ admits an unbounded 1-cocycle into its left regular representation, or (b) $Γ$ is an arbitrary wreath product group with amenable base.作为这些结果的副产品，我们获得了w $^*$ - 超级群体和新的刚性的新示例，并在c $^*$ - 代数理论中获得了新的刚性。
We provide a new large class of countable icc groups $\mathcal A$ for which the product rigidity result from [CdSS15] holds: if $Γ_1,\dots,Γ_n\in\mathcal A$ and $Λ$ is any group such that $L(Γ_1\times\dots\timesΓ_n)\cong L(Λ)$, then there exists a product decomposition $Λ=Λ_1\times\dots\times Λ_n$ such that $L(Λ_i)$ is stably isomorphic to $L(Γ_i)$, for any $1\leq i\leq n$. Class $\mathcal A$ consists of groups $Γ$ for which $L(Γ)$ admits an s-malleable deformation in the sense of Sorin Popa and it includes all non-amenable groups $Γ$ such that either (a) $Γ$ admits an unbounded 1-cocycle into its left regular representation, or (b) $Γ$ is an arbitrary wreath product group with amenable base. As a byproduct of these results, we obtain new examples of W$^*$-superrigid groups and new rigidity results in the C$^*$-algebra theory.
