Tight inclusions of $C^*$-dynamical systems

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2023-10-14 DOI:10.4171/ggd/739

Yair Hartman, Mehrdad Kalantar

引用次数: 0

Abstract

We study a notion of tight inclusions of $C^$- and $W^$-dynamical systems, which is meant to capture a tension between topological and measurable rigidity of boundary actions. An important case of such inclusions is $C(X)\subset L^\infty(X, \nu)$ for measurable boundaries with unique stationary compact models. We discuss the implications of this phenomenon in the description of Zimmer amenable intermediate factors. Furthermore, we prove applications in the problem of maximal injectivity of von Neumann algebras.

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$C^*$-动力系统的紧密内含

我们研究了$C^$ -和$W^$ -动力系统的紧包涵的概念，这意味着捕获边界作用的拓扑刚性和可测量刚性之间的张力。这种内含物的一个重要例子是$C(X)\subset L^\infty(X, \nu)$对于具有唯一平稳紧模型的可测量边界。我们在描述齐默可服从的中间因素时讨论了这一现象的含义。进一步证明了该方法在冯诺依曼代数最大注入性问题中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.