### Abstract

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

Pages (from-to) | 613-643 |

Number of pages | 31 |

Journal | Houston Journal of Mathematics |

Volume | 44 |

Issue number | 2 |

Publication status | Published - 2018 |

### Fingerprint

### Keywords

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

### Cite this

*Houston Journal of Mathematics*,

*44*(2), 613-643.

**Rokhlin dimension for C*-correspondences.** / Brown, Nathanial P.; Tikuisis, Aaron; Zelenberg, Aleksey M.

Research output: Contribution to journal › Article

*Houston Journal of Mathematics*, vol. 44, no. 2, pp. 613-643.

}

TY - JOUR

T1 - Rokhlin dimension for C*-correspondences

AU - Brown, Nathanial P.

AU - Tikuisis, Aaron

AU - Zelenberg, Aleksey M.

N1 - N.B. and A.Z. were partially supported by NSF grant DMS-1201385. A.T. was partially supported by an NSERC Postdoctoral Fellowship and EPSRC grant EP/N00874X/1.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Nuclear C∗-algebras

KW - C∗-correspondences

KW - nuclear dimension

KW - Rokhlin property

KW - Rokhlin dimension

M3 - Article

VL - 44

SP - 613

EP - 643

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

SN - 0362-1588

IS - 2

ER -