### Abstract

We consider a certain class of unital simple stably finite C*-algebras which absorb the Jiang-Su algebra Z tensorially. Under a mild assumption, we show that the crossed product of a C*-algebra in this class by a strongly outer action of ℤ ^{N} or a finite group is Z -stable. As an application, we also prove that all strongly outer actions of ℤ ^{2} on Z are mutually cocycle conjugate.

Original language | English |
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Pages (from-to) | 193-228 |

Number of pages | 36 |

Journal | Communications in Mathematical Physics |

Volume | 314 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 1 2012 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Matui, H., & Sato, Y. (2012). Z-Stability of Crossed Products by Strongly Outer Actions.

*Communications in Mathematical Physics*,*314*(1), 193-228. https://doi.org/10.1007/s00220-011-1392-9