AF C^-algebras from non-AF groupoids

AF C^-algebras from non-AF groupoids

We construct ample groupoids from certain categories of paths, and prove that their C^*-algebras coincide with the continued fraction approximately finite dimensional (AF) algebras of Effros and Shen. The proof relies on recent classification results for simple nuclear C^*-algebras. The groupoids ar...

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Veröffentlicht in:Transactions of the American Mathematical Society 2022-10, Vol.375 (10), p.7323
Hauptverfasser: Ian Mitscher, Jack Spielberg
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Jack Spielberg
description We construct ample groupoids from certain categories of paths, and prove that their C^*-algebras coincide with the continued fraction approximately finite dimensional (AF) algebras of Effros and Shen. The proof relies on recent classification results for simple nuclear C^*-algebras. The groupoids are not principal. This provides examples of Cartan subalgebras in the continued fraction AF algebras that are isomorphic, but not conjugate, to the standard diagonal subalgebras.
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title AF C^-algebras from non-AF groupoids
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