Inverse Semigroups and Sheu's Groupoid for the Odd Dimensional Quantum Spheres

http://dx.doi.org/10.4153/CMB-2011-191-x
10 pages

  Published:2012-01-03
 

In this paper, we give a different proof of the fact that the odd dimensional quantum spheres are groupoid $C^{*}$-algebras. We show that the $C^{*}$-algebra $C(S_{q}^{2\ell+1})$ is generated by an inverse semigroup $T$ of partial isometries. We show that the groupoid $\mathcal{G}_{tight}$ associated with the inverse semigroup $T$ by Exel is exactly the same as the groupoid considered by Sheu.