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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Reconstructing a totally disconnected groupoid from its ample semigroup


Author: R. Exel
Journal: Proc. Amer. Math. Soc. 138 (2010), 2991-3001
MSC (2010): Primary 22A22, 20M18, 20M30, 46L55
Published electronically: April 8, 2010
MathSciNet review: 2644910
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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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Additional Information

R. Exel
Affiliation: Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Brasil
Email: r@exel.com.br

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10346-3
PII: S 0002-9939(10)10346-3
Received by editor(s): September 17, 2009
Received by editor(s) in revised form: November 30, 2009
Published electronically: April 8, 2010
Additional Notes: The author was partially supported by CNq.
Communicated by: Marius Junge
Article copyright: © Copyright 2010 Ruy Exel