Co-universal C*-algebras associated to generalised graphs

@article{Brownlowe2010CouniversalCA,
  title={Co-universal C*-algebras associated to generalised graphs},
  author={Nathan Brownlowe and Aidan Sims and Sean T. Vittadello},
  journal={Israel Journal of Mathematics},
  year={2010},
  volume={193},
  pages={399-440}
}
We introduce P-graphs, which are generalisations of directed graphs in which paths have a degree in a semigroup P rather than a length in ℕ. We focus on semigroups P arising as part of a quasi-lattice ordered group (G, P) in the sense of Nica, and on P-graphs which are finitely aligned in the sense of Raeburn and Sims. We show that each finitely aligned P-graph admits a C*-algebra C*min (Λ) which is co-universal for partialisometric representations of Λ which admit a coaction of G compatible… 

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