## Abstract

We introduce the notion of a homotopy of product systems, and show that the Cuntz-Nica-Pimsner algebras of homotopic product systems over N^{k} have isomorphic K-theory. As an application, we give a new proof that the K-theory of a 2-graph C^{*}-algebra is independent of the factorisation rules, and we further show that the K-theory of any twisted 2-graph C^{*}-algebra is independent of the twisting 2-cocycle. We also explore applications to K-theory for the C^{*}-algebras of single-vertex k-graphs, reducing the question of whether the K-theory is independent of the factorisation rules to a question about path-connectedness of the space of solutions to an equation of Yang-Baxter type.

Original language | English |
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Pages (from-to) | 307-338 |

Number of pages | 32 |

Journal | Indiana University Mathematics Journal |

Volume | 71 |

Issue number | 5 |

DOIs | |

State | Published - 2022 |

## Keywords

- Cuntz-Nica-Pimsner
- higher-rank graph
- K-theory
- Product system