Co-universal C*-algebras associated to generalised graphs

Details Co-universal C*-algebras associated to generalised graphs Co-universal C*-algebras associated to generalised graphs

2010-09-07

arxiv.org/abs/1009.1184v1

Mathematics

Operator Algebras

29 pages; 1 picture prepared in TiKZ

Scientific paper

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}(Lambda) which is co-universal for partial-isometric representations of Lambda 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 C*_{min}(Lambda) for some (N^2 * N)-graph Lambda.

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