论文标题
在不变的von Neumann sublgebras僵化属性上
On invariant von Neumann subalgebras rigidity property
论文作者
论文摘要
我们说，如果每个$γ$ - 不变的von neumann subalgebra $ \ neumant subalgebra $ \ Mathcal {m} $ in $ l（γ）$，则可以满足不变的von neumann sublgebras刚性（ISR）属性不变的von neumann subalgebras刚性（ISR）属性，以满足不可数量的离散$γ$，$ l（γγ）$ in $ l（γ）$，如果每一个属性满足不变性的，那么一个可数的$γ$。我们显示了许多``负弯曲的''组，包括所有无扭转的非扭曲群体和无扭转的群体和无扭转的组，在温和的假设下具有正面$ l^2 $ -betti数字，并且它们的某些有限直接乘积具有此属性。我们还讨论了是否可以放宽无扭转假设。
We say that a countable discrete group $Γ$ satisfies the invariant von Neumann subalgebras rigidity (ISR) property if every $Γ$- invariant von Neumann subalgebra $\mathcal{M}$ in $L(Γ)$ is of the form $L(Λ)$ for some normal subgroup $Λ\lhd Γ$. We show many ``negatively curved" groups, including all torsion free non-amenable hyperbolic groups and torsion free groups with positive first $L^2$-Betti number under a mild assumption, and certain finite direct product of them have this property. We also discuss whether the torsion-free assumption can be relaxed.
