论文标题
关于相对Biexact组的结构von Neumann代数
On the structure of relatively biexact group von Neumann algebras
论文作者
论文摘要
使用$ \ mathbb {b}（l^2m）$的双交易中的计算，我们在von Neumann代数级别开发了一种新技术，以升级相对适当的近端到完全正确的接近性。这用于在结构上对$lγ$的子代理进行分类，其中$γ$是一个无限的组，相对于有限的子组$ \ {λ_i\} _ {i \ in I} $的有限家族，因此每个$λ_i$几乎是$γ$。这概括了\ cite {dkep21}的结果，该结果对biexact组的von neumann代数的亚代代代数进行了分类。通过与Popa的变形 - 戒头理论的技术相结合，在适当近端的von Neumann代数的情况下，我们获得了免费产品的新结构吸收定理和广义的黑素型定理。
Using computations in the bidual of $\mathbb{B}(L^2M)$ we develop a new technique at the von Neumann algebra level to upgrade relative proper proximality to full proper proximality. This is used to structurally classify subalgebras of $LΓ$ where $Γ$ is an infinite group that is biexact relative to a finite family of subgroups $\{Λ_i\}_{i\in I}$ such that each $Λ_i$ is almost malnormal in $Γ$. This generalizes the result of \cite{DKEP21} which classifies subalgebras of von Neumann algebras of biexact groups. By developing a combination with techniques from Popa's deformation-rigidity theory we obtain a new structural absorption theorem for free products and a generalized Kurosh type theorem in the setting of properly proximal von Neumann algebras.
