Reconstructing a totally disconnected groupoid from its ample semigroup

Exel, R.

doi:10.1090/S0002-9939-10-10346-3

Reconstructing a totally disconnected groupoid from its ample semigroup
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by R. Exel PDF

Proc. Amer. Math. Soc. 138 (2010), 2991-3001

Abstract:

We show that a (not necessarily Hausdorff) étale, second countable groupoid $\mathcal {G}$ with totally disconnected unit space may be reconstructed solely from the algebraic structure of its ample semigroup $\mathcal {S}$. We also show that $C^*(\mathcal {G})$ possesses a universal property related to tight representations of $\mathcal {S}$.

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