Fell bundles associated to groupoid morphisms
| dc.creator | Deaconu, Valentin | |
| dc.creator | Kumjian, Alex | |
| dc.creator | Ramazan, Birant | |
| dc.date | 2006-12-23 | |
| dc.date | 2007-07-14 | |
| dc.date.accessioned | 2026-07-07T08:17:25Z | |
| dc.date.available | 2026-07-07T08:17:25Z | |
| dc.description | Given a continuous open surjective morphism $π:G\to H$ 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 $H^0$. 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. | |
| dc.description | 12 pages, revised version, references added; to appear in Mathematica Scandinavica | |
| dc.identifier | https://arxiv.org/abs/math/0612746 | |
| dc.identifier | http://arxiv.org/abs/math/0612746 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134086 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05 (Primary); 46L55 (Secondary) | |
| dc.title | Fell bundles associated to groupoid morphisms | |
| dc.type | text |