Non-Hausdorff groupoids

Ruy Exel

Non-Hausdorff groupoids

Operator Algebras 2009-11-23 v3 Dynamical Systems

Authors: Ruy Exel

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.

Keywords

c*-algebra c*-algebras group theory

Cite

@article{arxiv.0812.4087,
  title  = {Non-Hausdorff groupoids},
  author = {Ruy Exel},
  journal= {arXiv preprint arXiv:0812.4087},
  year   = {2009}
}

Comments

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

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