The Mackey Machine for Crossed Products by Regular Groupoids. II

Details The Mackey Machine for Crossed Products by Regular Groupoids. II The Mackey Machine for Crossed Products by Regular Groupoids. II

2009-08-11

arxiv.org/abs/0908.1434v2

Mathematics

Operator Algebras

Results have been extended to groupoids with potentially nonabelian stabilizers, 18 pages

Scientific paper

We prove that given a regular groupoid $G$ whose isotropy subgroupoid $S$ has a Haar system, along with a dynamical system $(A,G,\alpha)$, there is an action of $G$ on the spectrum of $A\rtimes S$ such that the spectrum of $A\rtimes G$ is homeomorphic to the orbit space of this action via induction. In addition, we give a strengthening of these results in the case where the crossed product is a groupoid algebra.

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