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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