Abstract
We consider a certain class of unital simple stably finite C*-algebras which absorb the Jiang-Su algebra \({\mathcal {Z}}\) tensorially. Under a mild assumption, we show that the crossed product of a C*-algebra in this class by a strongly outer action of \({\mathbb{Z}^N}\) or a finite group is \({\mathcal {Z}}\) -stable. As an application, we also prove that all strongly outer actions of \({\mathbb {Z}^2}\) on \({\mathcal {Z}}\) are mutually cocycle conjugate.
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Communicated by Y. Kawahigashi
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Matui, H., Sato, Y. \({\mathcal {Z}}\) -Stability of Crossed Products by Strongly Outer Actions. Commun. Math. Phys. 314, 193–228 (2012). https://doi.org/10.1007/s00220-011-1392-9
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DOI: https://doi.org/10.1007/s00220-011-1392-9