约化群胚C*-代数简单性的刻画
A characterization of simplicity of reduced groupoid C*-algebras
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中文总结 AI 辅助
本文刻画了约化群胚C*-代数的简单性，证明其等价于存在余稠密单位点集具有C*-简单迷向群，并构造反例回答Christensen和Neshveyev的问题。
中文摘要 AI 辅助
我们证明，对于具有紧单位空间的第二可数局部紧Hausdorff étale极小群胚，约化群胚C*-代数的简单性蕴含存在一个单位点的余稠密集合，其迷向群具有C*-简单性。将此结果与Christensen和Neshveyev关于迷向群代数 exotic 完备化的研究相结合，我们证明逆蕴含也成立。最后，我们构造一个Hausdorff étale极小群胚，其迷向群的诱导 exotic 完备化不同于其约化群C*-代数，回答了Christensen和Neshveyev的一个问题。
英文摘要
We show that, for a second-countable locally compact Hausdorff étale minimal groupoid with compact unit space, simplicity of the reduced groupoid C*-algebra implies the existence of a comeager set of unit points with C*-simple isotropy group. Combining this result with work of Christensen and Neshveyev on exotic completions of isotropy group algebras, we show that the converse implication is also true. Finally, we construct a Hausdorff étale minimal groupoid with an isotropy group whose induced exotic completion differs from its reduced group C*-algebra, answering a question of Christensen and Neshveyev.
发表机构
- Chalmers University of Technology（查尔姆斯理工大学）
- University of Gothenburg（哥德堡大学）
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