拓扑图代数上的三角形权重

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2024-03-05 DOI:10.1017/etds.2024.20

JOHANNES CHRISTENSEN

引用次数: 0

摘要

我们描述了第二可数拓扑图 E 的边界路径空间 $\partial E$ 上的两种正则不变度量，这使我们能够描述 $C^{*}(E)$ 上所有不是轨距不变的极值三边权重。利用这一描述，我们证明了当第二个可数拓扑图 E 的 C$^{*}$ 代数 $C^{*}(E)$ 是自由的时候，其上的所有三项权重都是轨距不变的。这尤其意味着，当$C^{*}(E)$是简单可分的时候，$C^{*}(E)$上的所有三项权重都是规整不变的。

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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Tracial weights on topological graph algebras

We describe two kinds of regular invariant measures on the boundary path space $\partial E$ of a second countable topological graph E, which allows us to describe all extremal tracial weights on $C^{*}(E)$ which are not gauge-invariant. Using this description, we prove that all tracial weights on the C$^{*}$-algebra $C^{*}(E)$ of a second countable topological graph E are gauge-invariant when E is free. This in particular implies that all tracial weights on $C^{*}(E)$ are gauge-invariant when $C^{*}(E)$ is simple and separable.

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来源期刊

Ergodic Theory and Dynamical Systems 数学-数学

CiteScore

1.70

自引率

11.10%

发文量

113

审稿时长

6-12 weeks

期刊介绍： Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.