کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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5778538 | 1633772 | 2017 | 25 صفحه PDF | دانلود رایگان |

In this paper, we accomplish two objectives. Firstly, we extend and improve some results in the theory of (semi-)strongly self-absorbing Câ-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 Câ-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.
Journal: Advances in Mathematics - Volume 316, 20 August 2017, Pages 356-380