Simplicity of algebras associated to étale groupoids

Details Simplicity of algebras associated to étale groupoids Simplicity of algebras associated to étale groupoids

2012-04-14

arxiv.org/abs/1204.3127v1

Mathematics

Operator Algebras

20 pages

Scientific paper

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.

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