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

Published:2012-01-03
Printed: Sep 2013
• S. Sundar,
Indian Statistical Institute, Delhi, India
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Abstract

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 spheres
 MSC Classifications: 46L99 - None of the above, but in this section 20M18 - Inverse semigroups