• DOI:10.1007/S11856-012-0106-0
• Corpus ID: 119259971

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}
}

• Nathan Brownlowe, A. Sims, Sean T. Vittadello
• Published 7 September 2010
• Mathematics
• Israel Journal of Mathematics

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 with the P-valued length function. We also characterise when a homomorphism induced by the co-universal property is injective. Our results combined with those of Spielberg show that every Kirchberg algebra is Morita equivalent to C*min (Λ) for some (ℕ2* ℕ)-graph Λ.