## Abstract

In this paper we study Cuntz–Pimsner algebras associated to C^{∗}-correspondences over commutative C^{∗}-algebras from the point of view of the C^{∗}-algebra classification programme. We show that when the correspondence comes from an aperiodic homeomorphism of a finite dimensional infinite compact metric space X twisted by a vector bundle, the resulting Cuntz–Pimsner algebras have finite nuclear dimension. When the homeomorphism is minimal, this entails classification of these C^{∗}-algebras by the Elliott invariant. This establishes a dichotomy: when the vector bundle has rank one, the Cuntz–Pimsner algebra has stable rank one. Otherwise, it is purely infinite. For a Cuntz–Pimsner algebra of a minimal homeomorphism of an infinite compact metric space X twisted by a line bundle over X, we introduce orbit-breaking subalgebras. With no assumptions on the dimension of X, we show that they are centrally large subalgebras and hence simple and stably finite. When the dimension of X is finite, they are furthermore Z-stable and hence classified by the Elliott invariant.

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

Pages (from-to) | 1597-1640 |

Number of pages | 44 |

Journal | Transactions of the American Mathematical Society |

Volume | 377 |

Issue number | 3 |

DOIs | |

State | Published - 1 Mar 2024 |

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics

## Fingerprint

Dive into the research topics of 'C^{∗}-ALGEBRAS ASSOCIATED TO HOMEOMORPHISMS TWISTED BY VECTOR BUNDLES OVER FINITE DIMENSIONAL SPACES'. Together they form a unique fingerprint.