## Abstract

We consider the boundary-path groupoids of topological higher-rank graphs. We show that all such groupoids are topologically amenable. We deduce that the *C*^{∗} -algebras of topological higher-rank graphs are nuclear and prove versions of the gauge-invariant uniqueness theorem and the Cuntz–Krieger uniqueness theorem. We then provide a necessary and sufficient condition for simplicity of a topological higher-rank graph *C*^{∗} -algebra, and a condition under which it is also purely infinite.

Original language | English |
---|---|

Pages (from-to) | 669-684 |

Number of pages | 16 |

Journal | Proceedings of the American Mathematical Society |

Volume | 146 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2018 |

Externally published | Yes |

## Fingerprint

Dive into the research topics of 'Uniqueness theorems for topological higher-rank graph*C*

^{∗}-algebras'. Together they form a unique fingerprint.