The Mackey Machine for Crossed Products by Regular Groupoids. II

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Goehle, Geoff
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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.
Comment: Results have been extended to groupoids with potentially nonabelian stabilizers, 18 pages
Keywords
Mathematics - Operator Algebras, 47L65, 47A67
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