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Non-Hausdorff étale groupoids

Author: R. Exel
Journal: Proc. Amer. Math. Soc. 139 (2011), 897-907
MSC (2010): Primary 46L55; Secondary 22A22
Published electronically: October 28, 2010
MathSciNet review: 2745642
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Abstract: We present examples of non-Hausdorff, étale, essentially principal groupoids for which three results, known to hold in the Hausdorff case, fail. These results are: (A) the subalgebra of continuous functions on the unit space is maximal abelian within the reduced groupoid C*-algebra, (B) every nonzero ideal of the reduced groupoid C*-algebra has a nonzero intersection with the subalgebra of continuous functions on the unit space, and (C) the open support of a normalizer is a bisection.

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Additional Information

R. Exel
Affiliation: Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Brazil

Keywords: Non-Hausdorff groupoids, essentially principal groupoids
Received by editor(s): July 30, 2009
Published electronically: October 28, 2010
Additional Notes: The author was partially supported by CNPq.
Communicated by: Marius Junge
Article copyright: © Copyright 2010 Ruy Exel

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