The C*-algebras of arbitrary graphs
Operator Algebras
2007-05-23 v3
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.
Keywords
Cite
@article{arxiv.math/0009228,
title = {The C*-algebras of arbitrary graphs},
author = {D. Drinen and M. Tomforde},
journal= {arXiv preprint arXiv:math/0009228},
year = {2007}
}
Comments
19 pages, uses XY-pic. New version comments: This is the published version. A few small typos from the previous version are corrected