Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46L55, 22A22

Retrieve articles in all journals with MSC (2010): 46L55, 22A22


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10477-X
PII: S 0002-9939(2010)10477-X
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