Iterated crossed products for groupoid fibrations

2016/04/07 by Alcides Buss, Ralf Meyer, Buss, Alcides +1
Mathematics · #22A22 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1604.02015

openalex publication_date 2016/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and study fibrations of topological groupoids. We interpret a groupoid fibration L->H with fibre G as an action of H on G by groupoid equivalences. Our main result shows that a crossed product for an action of L is isomorphic to an iterated crossed product first by G and then by H. Here groupoid action means a Fell bundle over the groupoid, and crossed product means the section C*-algebra.

Citations

• Fell bundles over inverse semigroups and twisted etale groupoids
• Coactions and Fell bundles
• Higher Groupoid Actions, Bibundles, and Differentiation

Related

• Groupoid equivalence and the associated iterated crossed product
• Groupoid Semidirect Product Fell Bundles I- Actions by Isomorphisms
• Groupoid Crossed Products
• Groupoid Crossed Products of Continuous-Trace C*-Algebras
• Fell bundles associated to groupoid morphisms