Abstract
We construct ample groupoids from certain categories of paths, and prove that their C â 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 â 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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