Simplicity of twisted C*algebras of DeaconuRenault groupoids
Abstract
We consider DeaconuRenault groupoids associated to actions of finiterank free abelian monoids by local homeomorphisms of locally compact Hausdorff spaces. We study simplicity of the twisted C*algebra of such a groupoid determined by a continuous circlevalued groupoid 2cocycle. When the groupoid is not minimal, this C*algebra is never simple, so we focus on minimal groupoids. We describe an action of the quotient of the groupoid by the interior of its isotropy on the spectrum of the twisted C*algebra of the interior of the isotropy. We prove that the twisted groupoid C*algebra is simple if and only if this action is minimal. We describe applications to crossed products of topologicalgraph C*algebras by quasifree actions.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.02583
 Bibcode:
 2021arXiv210902583A
 Keywords:

 Mathematics  Operator Algebras;
 46L05
 EPrint:
 Corrected the definition of a bicharacter. 40 pages