### Abstract

We extend the notion of Rokhlin dimension from topological dynamical systems to C∗-correspondences. We show that in the presence of finite Rokhlin dimension and a mild quasidiagonal-like condition (which, for example, is automatic for finitely generated projective correspondences), finite nuclear dimension passes from the scalar algebra to the associated Toeplitz–Pimsner and (hence) Cuntz–Pimsner algebras. As a consequence we provide new examples of classifiable C∗-algebras: if A is simple, unital, has finite nuclear dimension and satisfies the UCT, then for every finitely generated projective H with finite Rokhlin dimension, the associated Cuntz–Pimsner algebra O(H) is classifiable in the sense of Elliott’s Program.

Original language | English |
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Pages (from-to) | 613-643 |

Number of pages | 31 |

Journal | Houston Journal of Mathematics |

Volume | 44 |

Issue number | 2 |

Publication status | Published - 2018 |

### Keywords

- Nuclear C∗-algebras
- C∗-correspondences
- nuclear dimension
- Rokhlin property
- Rokhlin dimension

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## Cite this

Brown, N. P., Tikuisis, A., & Zelenberg, A. M. (2018). Rokhlin dimension for C*-correspondences.

*Houston Journal of Mathematics*,*44*(2), 613-643. https://arxiv.org/abs/1608.03214v1