The graph groupoid of a quantum sphere
Operator Algebras
2026-05-01 v3 Mathematical Physics
Differential Geometry
math.MP
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.
Cite
@article{arxiv.2407.02169,
title = {The graph groupoid of a quantum sphere},
author = {Francesco D'Andrea},
journal= {arXiv preprint arXiv:2407.02169},
year = {2026}
}
Comments
17 pages; v3: minor corrections