论文标题
算术组的魅力性和刚度
Charmenability and Stiffness of Arithmetic Groups
论文作者
论文摘要
我们表征了算术组之间的魅力性，并推断出与正常亚组，特征，动力学，表示和相关操作员代数有关的二分法陈述。我们通过研究固定动力学的固定动力学来做到这一点，尤其是我们确定刚度：任何固定概率度量都是不变的。这概括了Furstenberg的经典结果，用于圆环上的动态。在较高的等级假设下，我们表明，在有限生成的虚拟型组的字符空间上的任何动作都很僵硬。
We characterize charmenability among arithmetic groups and deduce dichotomy statements pertaining normal subgroups, characters, dynamics, representations and associated operator algebras. We do this by studying the stationary dynamics on the space of characters of the amenable radical, and in particular we establish stiffness: any stationary probability measure is invariant. This generalizes a classical result of Furstenberg for dynamics on the torus. Under a higher rank assumption, we show that any action on the space of characters of a finitely generated virtually nilpotent group is stiff.
