Non-Hausdorff groupoids

Details Non-Hausdorff groupoids Non-Hausdorff groupoids

2008-12-22

arxiv.org/abs/0812.4087v3

Mathematics

Operator Algebras

12 pages, no figures. An entirely new section was added with an example showing that it is impossible to reconstruct a non-Hau

Scientific paper

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.

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