Reconstructing a totally disconnected groupoid from its ample semigroup
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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 $\mathcal {S}$.References
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Additional Information
- R. Exel
- Affiliation: Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Brasil
- MR Author ID: 239607
- Email: r@exel.com.br
- 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
- © Copyright 2010 Ruy Exel
- Journal: Proc. Amer. Math. Soc. 138 (2010), 2991-3001
- MSC (2010): Primary 22A22, 20M18, 20M30, 46L55
- DOI: https://doi.org/10.1090/S0002-9939-10-10346-3
- MathSciNet review: 2644910