# 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} }

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…

## 17 Citations

### Groupoid actions on $C^*$-correspondences

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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…

### Group actions on graphs and $C^*$-correspondences

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### Cuntz-Pimsner algebras of group representations

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### Semicrossed Products of Operator Algebras by Semigroups

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We examine Nica-Pimsner algebras associated with semigroup actions of $\mathbb{Z}_+^n$ on a C*-algebra $A$ by $*$-endomorphisms. We give necessary and sufficient conditions on the dynamics for…

### Contributions to the theory of C*-correspondences with applications to multivariable dynamics

- Mathematics
- 2011

Motivated by the theory of tensor algebras and multivariable C*-dynamics, we revisit two fundamental techniques in the theory of C*-correspondences, the "addition of a tail" to a non-injective…

### Product systems and their representations: an approach using Fock spaces and Fell bundles

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In this exposition we highlight product systems as the semigroup analogue of Fell bundles. Motivated by Fock creation operators we extend the definition of Fowler’s product systems over unital…

### Operator algebras for higher rank analysis and their application to factorial languages

- MathematicsJournal d'Analyse Mathématique
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We study strong compactly aligned product systems of ℤ+N over a C*-algebra A. We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of A.…

### Operator algebras for higher rank analysis and their application to factorial languages

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We study strong compactly aligned product systems of ℤ + N over a C*-algebra A . We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of A .…

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