The orbit space of groupoids whose $C^*$-algebras are GCR

Daniel W van Wyk

The orbit space of groupoids whose $C^*$-algebras are GCR

Operator Algebras 2017-09-12 v1

Authors: Daniel W van Wyk

Abstract

Let $G$ be second countable locally compact Hausdorff groupoid with a continuous Haar system. We remove the assumption of amenability in a theorem by Clark about GCR groupoid $C^*$ -algebras. We show that if the groupoid $C^*$ -algebra of $G$ is GCR then the orbits of $G$ are locally closed.

Keywords

groupoids C*-algebras GCR orbit space locally closed orbits

Cite

@article{arxiv.1709.02871,
  title  = {The orbit space of groupoids whose $C^*$-algebras are GCR},
  author = {Daniel W van Wyk},
  journal= {arXiv preprint arXiv:1709.02871},
  year   = {2017}
}

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