Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Reconstructing a totally disconnected groupoid from its ample semigroup

Author(s): R. Exel
Journal: Proc. Amer. Math. Soc. 138 (2010), 2991-3001.
MSC (2010): Primary 22A22, 20M18, 20M30, 46L55
Posted: April 8, 2010
MathSciNet review: 2644910
Retrieve article in: PDF

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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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