## Abstract

For a directed graph E, we compute the K-theory of the C ^{*}-algebra C^{*}(E) from the Cuntz-Krieger generators and relations. First we compute the K-theory of the crossed product C^{*}(E) × γ T, and then using duality and the Pimsner-Voiculescu exact sequence we compute the K-theory of C ^{*}(E) ⊗K ≅ (C^{*}(E) × T) × ℤ. The method relies on the decomposition of C^{*}(E) as an inductive limit of Toeplitz graph C^{*}-algebras, indexed by the finite subgraphs of E. The proof and result require no special assumptions about the graph, and is given in graph-theoretic terms. This can be helpful if the graph is described by pictures rather than by a matrix.

Original language | English (US) |
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Pages (from-to) | 435-447 |

Number of pages | 13 |

Journal | Houston Journal of Mathematics |

Volume | 37 |

Issue number | 2 |

State | Published - Dec 26 2011 |

## Keywords

- Cuntz-Krieger algebra
- Directed graph
- Graph algebra

## ASJC Scopus subject areas

- Mathematics(all)