The graph groupoid of a quantum sphere

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.