具有Abelian各向同性的群拟C^*代数的原始理想空间

IF 1.2 2区数学 Q1 MATHEMATICS

Indiana University Mathematics Journal Pub Date : 2021-08-04 DOI:10.1512/iumj.2022.71.9523

D. W. V. Wyk, Dana P. Williams

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引用次数: 3

摘要

我们研究了具有阿贝尔各向同性的群胚的群胚C*代数的原始理想空间的拓扑。我们的结果包括具有阿贝兰稳定剂的作用类群的已知结果。此外，当各向同性映射除了跳跃不连续之外是连续的时，以及当G是由阿贝兰群丛固定的适当群胚的单位空间扩展时，我们得到了完整的结果。我们希望我们的方法将成为进一步取得这类成果的跳板。

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The primitive ideal space of groupoid C^*-algebras for groupoids with Abelian isotropy

We study the topology of the primitive ideal space of groupoid C∗algebras for groupoids with abelian isotropy. Our results include the known results for action groupoids with abelain stabilizers. Furthermore, we obtain complete results when the isotropy map is continuous except for jump discontinuities, and also when G is a unit space fixing extension of a proper groupoid by an abelain group bundle. We hope that our methods will be a springboard to further results of this type.

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