缩并自相似群的C*-代数的简单性

IF 2.6 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2025-09-01 DOI:10.1007/s00220-025-05411-5

Eusebio Gardella, Volodymyr Nekrashevych, Benjamin Steinberg, Alina Vdovina

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引用次数: 0

摘要

我们证明了Nekrashevych与一个收缩自相似群相关联的\(C^*\) -代数是简单的当且仅当对应的复\(*\) -代数是简单的。我们还改进了Steinberg和Szakács的算法，以确定\(*\) -代数是否简单。这提供了一类有趣的非hausdorff、可服从、有效和最小样本群，其中\(C^*\) -代数和复杂\(*\) -代数的简单性是等价的。

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Simplicity of C*-Algebras of Contracting Self-Similar Groups

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Simplicity of C*-Algebras of Contracting Self-Similar Groups

We show that the \(C^*\)-algebra associated by Nekrashevych to a contracting self-similar group is simple if and only if the corresponding complex \(*\)-algebra is simple. We also improve on Steinberg and Szakács’s algorithm to determine if the \(*\)-algebra is simple. This provides an interesting class of non-Hausdorff, amenable, effective and minimal ample groupoids for which simplicity of the \(C^*\)-algebra and the complex \(*\)-algebra are equivalent.

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.