# Graphs of $C^*$-correspondences and Fell bundles

@article{Deaconu2008GraphsO,
title={Graphs of \$C^*\$-correspondences and Fell bundles},
author={Valentin Deaconu and Alex Kumjian and David Pask and Aidan Sims},
journal={arXiv: Operator Algebras},
year={2008}
}
• Published 31 December 2008
• Mathematics
• arXiv: Operator Algebras
We define the notion of a $\Lambda$-system of $C^*$-correspondences associated to a higher-rank graph $\Lambda$. Roughly speaking, such a system assigns to each vertex of $\Lambda$ a $C^*$-algebra, and to each path in $\Lambda$ 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…
Let the groupoid $G$ with unit space $G^0$ act via a representation $\rho$ on a $C^*$-correspondence ${\mathcal H}$ over the $C_0(G^0)$-algebra $A$. By the universal property, $G$ acts on the
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