Cuntz-Krieger algebras of directed graphs

@inproceedings{PASK1996CuntzKriegerAO,
  title={Cuntz-Krieger algebras of directed graphs},
  author={ANDDAVID PASK and IAIN RAEBURNDepartment},
  year={1996}
}
  • ANDDAVID PASK, IAIN RAEBURNDepartment
  • Published 1996
We associate to each row-finite directed graph E a universal CuntzKrieger C∗-algebra C∗(E), and study how the distribution of loops in E affects the structure of C∗(E). We prove that C∗(E) is AF if and only if E has no loops. We describe an exit condition (L) on loops in E under which allows us to prove an analogue the CuntzKrieger uniqueness theorem and give a characterisation of when C∗(E) is purely infinite. If the graph E satisfies (L) and is cofinal, then we have a dichotomy: if E has no… CONTINUE READING
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