Non-Hausdorff groupoids
Abstract
We present examples of non-Hausdorff, etale, 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 bissection.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2008
- DOI:
- 10.48550/arXiv.0812.4087
- arXiv:
- arXiv:0812.4087
- Bibcode:
- 2008arXiv0812.4087E
- Keywords:
-
- Mathematics - Operator Algebras;
- Mathematics - Dynamical Systems;
- 46L55;
- 22A22
- E-Print:
- 12 pages, no figures. An entirely new section was added with an example showing that it is impossible to reconstruct a non-Hausdorff essentially principal groupoid as the germs for the action of the normalizers