The C*-algebras of arbitrary graphs

Abstract

To an arbitrary directed graph we associate a row-finite directed graph whose C*-algebra contains the C*-algebra of the original graph as a full corner. This allows us to generalize results for C*-algebras of row-finite graphs to C*-algebras of arbitrary graphs: the uniqueness theorem, simplicity criteria, descriptions of the ideals and primitive ideal space, and conditions under which a graph algebra is AF and purely infinite. Our proofs require only standard Cuntz-Krieger techniques and do not rely on powerful constructs such as groupoids, Exel-Laca algebras, or Cuntz-Pimsner algebras.

19 pages, uses XY-pic. New version comments: This is the published version. A few small typos from the previous version are corrected

Cited by in corpus (7)

• Computing K-theory and Ext for graph C*-algebras
• The ideal structure of the C*-algebras of infinite graphs
• Ideal structure of $C^{\ast }$-algebras associated with $C^{\ast }$-correspondences
• A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras I, fundamental results
• Stability of C*-algebras associated to graphs
• The primitive ideal space of the C*-algebras of infinite graphs
• A functorial approach to the C*-algebras of a graph