Graphs of $C^*$-correspondences and Fell bundles
| dc.creator | Deaconu, Valentin | |
| dc.creator | Kumjian, Alex | |
| dc.creator | Pask, David | |
| dc.creator | Sims, Aidan | |
| dc.date | 2008-12-31 | |
| dc.date | 2009-02-17 | |
| dc.date.accessioned | 2026-07-07T12:41:59Z | |
| dc.date.available | 2026-07-07T12:41:59Z | |
| dc.description | We define the notion of a $Λ$-system of $C^*$-correspondences associated to a higher-rank graph $Λ$. Roughly speaking, such a system assigns to each vertex of $Λ$ a $C^*$-algebra, and to each path in $Λ$ a $C^*$-correspondence in a way which carries compositions of paths to balanced tensor products of $C^*$-correspondences. Under some simplifying assumptions, we use Fowler's technology of Cuntz-Pimsner algebras for product systems of $C^*$-correspondences to associate a $C^*$-algebra to each $Λ$-system. We then construct a Fell bundle over the path groupoid $\Gg_Λ$ and show that the $C^*$-algebra of the $Λ$-system coincides with the reduced cross-sectional algebra of the Fell bundle. We conclude by discussing several examples of our construction arising in the literature. | |
| dc.description | To appear in Indiana Univ. Math. J | |
| dc.identifier | https://arxiv.org/abs/0901.0032 | |
| dc.identifier | http://arxiv.org/abs/0901.0032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219931 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05 | |
| dc.title | Graphs of $C^*$-correspondences and Fell bundles | |
| dc.type | text |