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\({\mathcal {Z}}\) -Stability of Crossed Products by Strongly Outer Actions

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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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Authors and Affiliations

  1. Graduate School of Science, Chiba University, Inage-ku, Chiba, 263-8522, Japan

    Hiroki Matui

  2. Department of Mathematics, Hokkaido University, Kita-ku, Sapporo, 060-0810, Japan

    Yasuhiko Sato

Authors
  1. Hiroki Matui
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  2. Yasuhiko Sato
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Correspondence to Hiroki Matui.

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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

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