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.© 2005 Rocky Mountain Mathematics Consortium.