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• W2065155387 abstract "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 $C^*$-algebra to each $Lambda$-system. We then construct a Fell bundle over the path groupoid $Gg_Lambda$ and show that the $C^*$-algebra of the $Lambda$-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." @default.
• W2065155387 created "2016-06-24" @default.
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• W2065155387 date "2008-12-31" @default.
• W2065155387 modified "2023-10-03" @default.
• W2065155387 title "Graphs of $C^*$-correspondences and Fell bundles" @default.
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• W2065155387 hasPublicationYear "2008" @default.
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