Simplicity of algebras associated to étale groupoids

Abstract

We prove that the C*-algebra of a second-countable, étale, 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.

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

References in corpus (3)

• Simplicity of C*-algebras associated to higher-rank graphs
• A groupoid generalization of Leavitt path algebras
• Examples of masas in C*-algebras

Cited by in corpus (1)

• Topological freeness for $\ast$-commuting covering maps