## Abstract

We prove that a graph C^{*}-algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six-term exact sequence in K-theory. We prove that a similar classification also holds for a graph C^{*}-algebra with a largest proper ideal that is an AF-algebra. Our results are based on a general method developed by the first named author with Restorff and Ruiz. As a key step in the argument, we show how to produce stability for certain full hereditary subalgebras associated to such graph C^{*}-algebras. We further prove that, except under trivial circumstances, a unique proper nontrivial ideal in a graph C^{*}-algebra is stable.

Original language | English |
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Journal | Mathematische Annalen |

Volume | 346 |

Issue number | 2 |

Pages (from-to) | 393-418 |

Number of pages | 26 |

ISSN | 0025-5831 |

DOIs | |

Publication status | Published - 1 Nov 2009 |