English

Simplicity of algebras associated to \'etale groupoids

Operator Algebras 2013-10-10 v2 Rings and Algebras

Abstract

We prove that the C*-algebra of a second-countable, \'etale, amenable groupoid is simple if and only if the groupoid is topologically principal and minimal. We also show that if G has totally disconnected unit space, then the associated complex *-algebra introduced by Steinberg is simple if and only if the interior of the isotropy subgroupoid of G is equal to the unit space and G is minimal.

Keywords

Cite

@article{arxiv.1204.3127,
  title  = {Simplicity of algebras associated to \'etale groupoids},
  author = {Jonathan H. Brown and Lisa Orloff Clark and Cynthia Farthing and Aidan Sims},
  journal= {arXiv preprint arXiv:1204.3127},
  year   = {2013}
}

Comments

The introduction has been updated and minor changes have been made throughout. To appear in Semigroup Forum