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arXiv · 2407.02169

The graph groupoid of a quantum sphere

Francesco D'Andrea
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Abstract

Quantum spheres are among the most studied examples of compact quantum spaces, described by C*-algebras which are Cuntz-Krieger algebras of a directed graph, as proved by Hong and Szyma\'nski in 2002. About five years earlier, in 1997, Sheu proved that the C*-algebra of a quantum sphere is a groupoid C*-algebra. Here we show that the path groupoid of the directed graph of Hong and Szyma\'nski is isomorphic to the groupoid discovered by Sheu.

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Francesco D'Andrea. 2024-06-26. The graph groupoid of a quantum sphere. https://arxiv.org/abs/2407.02169

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