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

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

2008-12-31

arxiv.org/abs/0901.0032v2

Mathematics

Operator Algebras

To appear in Indiana Univ. Math. J

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Graphs of $C^*$-correspondences and Fell bundles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Graphs of $C^*$-correspondences and Fell bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Graphs of $C^*$-correspondences and Fell bundles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-536161