Graphs of C*-correspondences and Fell bundles

We define the notion of a ˄-system of C*-correspondences associated to a higher-rank graph ˄. Roughly speaking, such a system assigns to each vertex of ˄ a C*- algebra, and to each path in ˄ 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 ˄-system. We then construct a Fell bundle over the path groupoid G˄ and show that the C*-algebra of the ˄-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.