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Co-universal C*-algebras associated to generalised graphs

Journal Article


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 Cmin* (Λ) for some (ℕ2* ℕ)-graph Λ. © 2012 Hebrew University Magnes Press.

UOW Authors


  •   Brownlowe, Nathan D. (external author)
  •   Sims, Aidan
  •   Vittadello, Sean T. (external author)

Publication Date


  • 2013

Citation


  • Brownlowe, N., Sims, A. & Vittadello, S. T. (2013). Co-universal C*-algebras associated to generalised graphs. Israel Journal of Mathematics, 193 (1), 399-440.

Scopus Eid


  • 2-s2.0-84876110881

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/714

Number Of Pages


  • 41

Start Page


  • 399

End Page


  • 440

Volume


  • 193

Issue


  • 1

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 Cmin* (Λ) for some (ℕ2* ℕ)-graph Λ. © 2012 Hebrew University Magnes Press.

UOW Authors


  •   Brownlowe, Nathan D. (external author)
  •   Sims, Aidan
  •   Vittadello, Sean T. (external author)

Publication Date


  • 2013

Citation


  • Brownlowe, N., Sims, A. & Vittadello, S. T. (2013). Co-universal C*-algebras associated to generalised graphs. Israel Journal of Mathematics, 193 (1), 399-440.

Scopus Eid


  • 2-s2.0-84876110881

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/714

Number Of Pages


  • 41

Start Page


  • 399

End Page


  • 440

Volume


  • 193

Issue


  • 1