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arxiv: 1904.07431 · v1 · pith:K7O3O2TFnew · submitted 2019-04-16 · 🧮 math.OA

All classifiable Kirchberg algebras are C^(ast)-algebras of ample groupoids

classification 🧮 math.OA
keywords algebraskirchbergalgebraamplecasespielbergamenablebuilds
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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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