Co-universal C*-algebras associated to generalised graphs
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- Brownlowe, N., Sims, A. & Vittadello, S.T. Isr. J. Math. (2013) 193: 399. doi:10.1007/s11856-012-0106-0
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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.