All classifiable Kirchberg algebras are $C^{\ast}$-algebras of ample groupoids

Lisa Orloff Clark; James Fletcher; Astrid an Huef

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arXiv · 1904.07431

All classifiable Kirchberg algebras are $C^{\ast}$-algebras of ample groupoids

Lisa Orloff Clark·James Fletcher·Astrid an Huef

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Abstract

In this note we show that every Kirchberg algebra in the UCT class is the $C^{\ast}$-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.

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Lisa Orloff Clark, James Fletcher, Astrid an Huef. 2019-04-16. All classifiable Kirchberg algebras are $C^{\ast}$-algebras of ample groupoids. https://arxiv.org/abs/1904.07431

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