• Corpus ID: 14754548

The co-universal C*-algebra of a row-finite graph

@article{Sims2008TheCC,
  title={The co-universal C*-algebra of a row-finite graph},
  author={Aidan Sims},
  journal={arXiv: Operator Algebras},
  year={2008},
  pages={507-524}
}

• A. Sims
• Published 13 September 2008
• Mathematics
• arXiv: Operator Algebras

Let E be a row-finite directed graph. We prove that there exists a C -algebra C min(E) with the following co-universal property: given any C -algebra B generated by a Toeplitz-Cuntz-Krieger E-family in which all the vertex projections are nonzero, there is a canonical ho- momorphism from B onto C min(E). We also identify when a homo- morphism from B to C min(E) obtained from the co-universal property is injective. When every loop in E has an entrance, C min(E) coincides with the graph C -algebra C (E), but in general, C min(E) is a quotient of C (E). We investigate the properties of C min(E) with emphasis on the utility of co-universality as the defining property of the algebra.