Work

The graph groupoid of an odd-dimensional Vaksman–Soibelman quantum sphere

Year: 2026

Type: article

Abstract: Quantum spheres are among the most studied examples of compact quantum spaces. In particular, the ( 2 n + 1 ) -dimensional quantum sphere of Vaksman and Soibelman is described by a C*-algebra that is the Cuntz–Krieger algebra of a directed graph, as proved by Hong and Szymański in 2002. A few years earlier, in 1997, Sheu proved that the same C*-algebra is isomorphic to the groupoid C*-algebra of an étale groupoid. Here we show that the path groupoid of the directed graph of Hong and Szymański is isomorphic to the groupoid discovered by Sheu.

Source: Differential Geometry and its Applications

DOI: 10.1016/j.difgeo.2026.102459

Author: Francesco D'Andrea

Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, University of Naples Federico II

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,740

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni, HORIZON EUROPE Marie Sklodowska-Curie Actions