## Abstract

We give necessary and sufficient conditions which a graph should satisfy in order for its associated C
^{*}-algebra to have a T
_{1} primitive ideal space. We give a description of which one-point sets in such a primitive ideal space are open, and use this to prove that any purely infinite graph C
^{*}-algebrapurely infinite graph C
^{*}-algebra purely infinite graph C
^{*}-algebra with a T
_{1} (in particular Hausdorff) primitive ideal space, is a c
_{0}-direct sum of Kirchberg algebra. Moreover, we show that graph C
^{*}-algebras with a T
_{1} primitive ideal space canonically may be given the structure of a C(ℕ̃)-algebra, and that isomorphisms of their ℕ̃-filtered K-theory (without coefficients) lift to E(ℕ̃)-equivalences, as defined by Dadarlat and Meyer.

Original language | English |
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Title of host publication | Operator Algebra and Dynamics - Nordforsk Network Closing Conference |

Publisher | Springer |

Publication date | 2013 |

Pages | 141-156 |

ISBN (Print) | 9783642394584 |

DOIs | |

Publication status | Published - 2013 |

Event | Operator Algebra and Dynamics, NordForsk Network Closing Conference - Gjáargarður, Gjogv, Faroe Islands Duration: 15. May 2012 → 20. May 2012 |

### Conference

Conference | Operator Algebra and Dynamics, NordForsk Network Closing Conference |
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Location | Gjáargarður |

Country/Territory | Faroe Islands |

City | Gjogv |

Period | 15/05/2012 → 20/05/2012 |

Series | Springer Proceedings in Mathematics & Statistics |
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Volume | 58 |

ISSN | 2194-1009 |

## Keywords

- Filtered K-theory
- Primitive ideal space

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