论文标题
产品组晶格定理的非公共因素定理
The noncommutative factor theorem for lattices in product groups
论文作者
论文摘要
我们证明了针对产品组密集预测的晶格的非交换性坏色因子定理。作为该结果和我们以前的工作的应用，我们获得了所有不可约定晶格的非交换性Margulis因子定理$γ<g $，在更高排名的半神经代数组中。也就是说，我们给出了所有中间体的von neumann submalgebras $ \ operatorName {l}（γ）（γ）\ subset m \ subset \ subset \ subset \ operatorname {l}（γ\ curvearrowrow g/p）边界。
We prove a noncommutative Bader-Shalom factor theorem for lattices with dense projections in product groups. As an application of this result and our previous works, we obtain a noncommutative Margulis factor theorem for all irreducible lattices $Γ< G$ in higher rank semisimple algebraic groups. Namely, we give a complete description of all intermediate von Neumann subalgebras $\operatorname{L}(Γ) \subset M \subset \operatorname{L}(Γ\curvearrowright G/P)$ sitting between the group von Neumann algebra and the group measure space von Neumann algebra associated with the action on the Furstenberg-Poisson boundary.
