## Abstract

Given a separated graph (E, C), there are two different C *-algebras associated to it: the full graph C *-algebra C *(E, C) and the reduced one Cred*(E,C). For a large class of separated graphs (E, C), we prove that Cred*(E,C) either is purely infinite simple or admits a faithful tracial state. The main tool we use to show pure infiniteness of reduced graph C *-algebras is a generalization to the amalgamated case of a result on purely infinite simple free products due to Dykema. © 2012 Elsevier Ltd.

Original language | English |
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Pages (from-to) | 493-508 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 393 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 Sept 2012 |

## Keywords

- Amalgamated free product
- Conditional expectation
- Graph c -algebra *
- Purely infinite
- Separated graph
- Simple

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