Charmenability of arithmetic groups of product type
Charmenability of arithmetic groups of product type
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DOI：
10.1007/s00222-022-01117-w
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发表时间：
2020-09
影响因子：
3.1
通讯作者：
U. Bader;R. Boutonnet;Cyril Houdayer;J. Peterson
中科院分区：
文献类型：
--
作者：
U. Bader;R. Boutonnet;Cyril Houdayer;J. Peterson
讨论了积型算术群的字符和正定函数空间的特殊性质及其相关动力学。将这些性质公理化，定义了可调性和可调性的概念，并研究了它们在给定群的拓扑动力学、遍历理论和酉表示理论中的应用。为此，我们研究了某些von Neumann代数之间的等变正规ucp映射的奇异性。我们的讨论也适用于作用于树的产物的群。
We discuss special properties of the spaces of characters and positive definite functions , as well as their associated dynamics, for arithmetic groups of product type. Axiomatizing these properties, we define the notions of charmenability and charfiniteness and study their applications to the topological dynamics, ergodic theory and unitary representation theory of the given groups. To do that, we study singularity properties of equivariant normal ucp maps between certain von Neumann algebras. We apply our discussion also to groups acting on product of trees.