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Co-universal C*-algebras associated to generalised graphs

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Applied Statistics, University of Wollongong, Austin Keane Building, Wollongong, NSW, 2522, Australia

    Nathan Brownlowe, Aidan Sims & Sean T. Vittadello

Authors
  1. Nathan Brownlowe
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  2. Aidan Sims
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  3. Sean T. Vittadello
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Corresponding author

Correspondence to Nathan Brownlowe.

Additional information

This research was supported by the Australian Research Council.

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Brownlowe, N., Sims, A. & Vittadello, S.T. Co-universal C*-algebras associated to generalised graphs. Isr. J. Math. 193, 399–440 (2013). https://doi.org/10.1007/s11856-012-0106-0

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  • DOI: https://doi.org/10.1007/s11856-012-0106-0

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