Inverse semigroups and Sheu's groupoid for the odd dimensional quantum spheres

TL;DR

This paper provides a new proof that the C*-algebra of odd-dimensional quantum spheres can be described as a groupoid C*-algebra, utilizing inverse semigroup theory to reconstruct Sheu's groupoid.

Contribution

It introduces a novel approach using inverse semigroups to reconstruct Sheu's groupoid for the quantum spheres' C*-algebra.

Findings

The C*-algebra of odd-dimensional quantum spheres is a groupoid C*-algebra.

Inverse semigroup theory effectively reconstructs Sheu's groupoid.

The new proof offers an alternative perspective on the algebraic structure of quantum spheres.

Abstract

In this paper, we give a different proof of the fact that the $C^{*}$ algebra of the odd dimensional quantum spheres is a groupoid $C*}$ algebra. We use the theory of inverse semigroups to reconstruct the groupoid given by Sheu in [6].