### Abstract

Several relations on graphs, including primitive equivalence, explosion equivalence and strong shift equivalence, are examined and shown to preserve either the graph groupoid, a construction of Kumjian, Pask, Raeburn, and Renault, or the groupoid of a pointed version of the graph. Thus these relations preserve either the isomorphism class or the Morita equivalence class of the graph C*-algebra, as defined by Kumjian, Pask, and Raeburn.

Original language | English (US) |
---|---|

Pages (from-to) | 209-229 |

Number of pages | 21 |

Journal | Journal of Operator Theory |

Volume | 45 |

Issue number | 1 |

State | Published - 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Explosion
- Graph C*-algebra
- Graph groupoid
- Primitive equivalence
- Strong shift equivalence

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Operator Theory*,

*45*(1), 209-229.

**C*-equivalences of graphs.** / Drinen, D.; Sieben, Nandor.

Research output: Contribution to journal › Article

*Journal of Operator Theory*, vol. 45, no. 1, pp. 209-229.

}

TY - JOUR

T1 - C*-equivalences of graphs

AU - Drinen, D.

AU - Sieben, Nandor

PY - 2001

Y1 - 2001

N2 - Several relations on graphs, including primitive equivalence, explosion equivalence and strong shift equivalence, are examined and shown to preserve either the graph groupoid, a construction of Kumjian, Pask, Raeburn, and Renault, or the groupoid of a pointed version of the graph. Thus these relations preserve either the isomorphism class or the Morita equivalence class of the graph C*-algebra, as defined by Kumjian, Pask, and Raeburn.

AB - Several relations on graphs, including primitive equivalence, explosion equivalence and strong shift equivalence, are examined and shown to preserve either the graph groupoid, a construction of Kumjian, Pask, Raeburn, and Renault, or the groupoid of a pointed version of the graph. Thus these relations preserve either the isomorphism class or the Morita equivalence class of the graph C*-algebra, as defined by Kumjian, Pask, and Raeburn.

KW - Explosion

KW - Graph C-algebra

KW - Graph groupoid

KW - Primitive equivalence

KW - Strong shift equivalence

UR - http://www.scopus.com/inward/record.url?scp=0040956495&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040956495&partnerID=8YFLogxK

M3 - Article

VL - 45

SP - 209

EP - 229

JO - Journal of Operator Theory

JF - Journal of Operator Theory

SN - 0379-4024

IS - 1

ER -