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.

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

References in corpus (2)

• Partial dynamical systems and C*-algebras generated by partial isometries
• Cartan subalgebras in C*-algebras

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