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