The C*-algebras of arbitrary graphs

Details The C*-algebras of arbitrary graphs The C*-algebras of arbitrary graphs

2000-09-26

arxiv.org/abs/math/0009228v3

Rocky Mountain J. Math. 35 (2005), 105-135

Mathematics

Operator Algebras

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

Scientific paper

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.

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