### Abstract

In this paper, we accomplish two objectives. Firstly, we extend and improve some results in the theory of (semi-)strongly self-absorbing ⁎C⁎-dynamical systems, which was introduced and studied in previous work. In particular, this concerns the theory when restricted to the case where all the semi-strongly self-absorbing actions are assumed to be unitarily regular, which is a mild technical condition. The central result in the first part is a strengthened version of the equivariant McDuff-type theorem, where equivariant tensorial absorption can be achieved with respect to so-called very strong cocycle conjugacy.Secondly, we establish completely new results within the theory. This mainly concerns how equivariantly Z-stable absorption can be reduced to equivariantly UHF-stable absorption with respect to a given semi-strongly self-absorbing action. Combining these abstract results with known uniqueness theorems due to Matui and Izumi–Matui, we obtain the following main result. If G is a torsion-free abelian group and D is one of the known strongly self-absorbing ⁎C⁎-algebras, then strongly outer G-actions on D are unique up to (very strong) cocycle conjugacy. This is new even for Z3-actions on the Jiang–Su algebra.

Original language | English |
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Pages (from-to) | 356-380 |

Number of pages | 25 |

Journal | Advances in Mathematics |

Volume | 316 |

Early online date | 24 Jul 2017 |

DOIs | |

Publication status | Published - 20 Aug 2017 |

### Keywords

- Strongly self-absorbing C*-algebra
- Noncommutative dynamical systems

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## Cite this

Szabo, G. (2017). Strongly self-absorbing C*-dynamical systems, III.

*Advances in Mathematics*,*316*, 356-380. https://doi.org/10.1016/j.aim.2017.06.008