论文标题
纯粹无限的本地紧凑型Hausdorffétalegropsoid及其$ C^*$ - 代数
Purely infinite locally compact Hausdorff étale groupoids and their $C^*$-algebras
论文作者
论文摘要
在本文中，我们介绍了属性，包括类固醇比较，纯净无限和矛盾的比较，以及一种新的代数工具，称为groupoid semogroup，用于局部紧凑的Hausdorff flytale gropsoids。我们显示这些新工具有助于建立减少的gropsoid $ c^*$ - 代数的纯粹无限。作为一种应用，我们显示了针对纯净无限性的稳定有限性的二分法，这些二分法是由局部紧凑的hausdorffétaletale tage ytale the taugations降低的群体固醇$ c^*$ - 最小的拓扑主体tobological toctial tocalagolotoid。这概括了Bönicke-Li和Rainone-SIMS获得的二分法。我们还研究了我们的悖论比较，$ n $填充财产和本地签约财产之间的关系，这些物品出现在本地紧凑的HausdorffétaleGroupoid中。
In this paper, we introduce properties including groupoid comparison, pure infiniteness and paradoxical comparison as well as a new algebraic tool called groupoid semigroup for locally compact Hausdorff étale groupoids. We show these new tools help establishing pure infiniteness of reduced groupoid $C^*$-algebras. As an application, we show a dichotomy of stably finiteness against pure infiniteness for reduced groupoid $C^*$-algebras arising from locally compact Hausdorff étale minimal topological principal groupoids. This generalizes the dichotomy obtained by Bönicke-Li and Rainone-Sims. We also study the relation among our paradoxical comparison, $n$-filling property and locally contracting property appeared in the literature for locally compact Hausdorff étale groupoids.
