Theoretical Statistics and Mathematics Unit, ISI Delhi

Inverse semigroups and the Cuntz-Li algebras

by S. Sundar

In this paper, we apply the theory of inverse semigroups to the $C^{*}$-algebra $U[\mathbb{Z}]$ considered by Cuntz. We show that the $C^{*}$-algebra $U[\mathbb{Z}]$ is generated by an inverse semigroup of partial isometries. We explicity identify the groupoid $\mathcal{G}_{tight}$ associated to the inverse semigroup and show that $\mathcal{G}_{tight}$ is exactly the same groupoid obtained by Cuntz and Li.

isid/ms/2011/15 [fulltext]

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