论冯-诺伊曼群代数的可变子代数

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-10-23 DOI:10.1016/j.jfa.2024.110718

Tattwamasi Amrutam , Yair Hartman , Hanna Oppelmayer

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引用次数: 0

摘要

我们从动力学的角度来研究可数群 Γ 的群 von Neumann 代数 L(Γ) 的子 von Neumann 代数。研究表明，L(Γ) 存在一个最大不变可变子代数。引入了子代数空间上的不变概率度量（IRAs）概念，类似于不变随机子群的概念。并证明了可变 IRA 在最大可变不变子代数上得到支持。

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On the amenable subalgebras of group von Neumann algebras

We approach the study of sub-von Neumann algebras of the group von Neumann algebra

L (Γ)

for countable groups Γ from a dynamical perspective. It is shown that

L (Γ)

admits a maximal invariant amenable subalgebra. The notion of invariant probability measures (IRAs) on the space of subalgebras is introduced, analogous to the concept of Invariant Random Subgroups. And it is shown that amenable IRAs are supported on the maximal amenable invariant subalgebra.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis