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All classifiable Kirchberg algebras are C∗-algebras of ample groupoids
Expositiones Mathematicae ( IF 0.8 ) Pub Date : 2019-07-17 , DOI: 10.1016/j.exmath.2019.06.001
Lisa Orloff Clark , James Fletcher , Astrid an Huef

In this note we show that every Kirchberg algebra in the UCT class is the C-algebra of a Hausdorff, ample, amenable and locally contracting groupoid. The non-unital case follows from Spielberg’s graph-based models for Kirchberg algebras. Our contribution is the unital case and our proof builds on Spielberg’s construction.



中文翻译:

所有可分类的Kirchberg代数都是 C-充足类群的代数

在本说明中,我们表明UCT类中的每个Kirchberg代数都是 C-Hausdorff的代数,充足,可适应且局部收缩的类群。斯皮尔伯格基于图的基尔希贝格代数模型是非单位情况。我们的贡献是单位案例,我们的证明建立在Spielberg的结构上。

更新日期:2019-07-17
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