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The C*-algebras of arbitrary graphs

D. Drinen·M. Tomforde
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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.

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D. Drinen, M. Tomforde. 2007-03-21. The C*-algebras of arbitrary graphs. https://arxiv.org/abs/math/0009228

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