2006/12/23 by Valentin Deaconu, Deaconu, Valentin, Alex Kumjian +3
Mathematics · #46L05 (Primary) #46L55 (Secondary) #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.math/0612746
openalex publication_date 2006/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a continuous open surjective morphism π:G→ H of étale groupoids with amenable kernel, we construct a Fell bundle E over H and prove that its C*-algebra C^*r(E) is isomorphic to C^*r(G). This is related to results of Fell concerning C*-algebraic bundles over groups. The case H=X, a locally compact space, was treated earlier by Ramazan. We conclude that C^*r(G) is strongly Morita equivalent to a crossed product, the C*-algebra of a Fell bundle arising from an action of the groupoid H on a C*-bundle over H0. We apply the theory to groupoid morphisms obtained from extensions of dynamical systems and from morphisms of directed graphs with the path lifting property. We also prove a structure theorem for abelian Fell bundles.