Simplicity of algebras associated to étale groupoids

@article{Brown2012SimplicityOA,
  title={Simplicity of algebras associated to {\'e}tale groupoids},
  author={Jonathan Henry Brown and Lisa Orloff Clark and Cynthia Farthing and Aidan Sims},
  journal={Semigroup Forum},
  year={2012},
  volume={88},
  pages={433-452}
}
We prove that the full C∗-algebra of a second-countable, Hausdorff, étale, amenable groupoid is simple if and only if the groupoid is both topologically principal and minimal. We also show that if G has totally disconnected unit space, then the complex ∗-algebra of its inverse semigroup of compact open bisections, as introduced by Steinberg, is simple if and only if G is both effective and minimal. 

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