Inverse Semigroups and Sheu's Groupoid for the Odd Dimensional Quantum Spheres 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. Keywords:inverse semigroups, groupoids, odd dimensional quantum spheresCategories:46L99, 20M18