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\({\mathbb{Z}}\)-Actions on AH Algebras and \({\mathbb{Z}^2}\)-Actions on AF Algebras

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Abstract

We consider \({\mathbb{Z}}\)-actions (single automorphisms) on a unital simple AH algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the Rohlin property under some technical assumptions. Moreover, two \({\mathbb{Z}}\)-actions with the Rohlin property on such a C*-algebra are shown to be cocycle conjugate if they are asymptotically unitarily equivalent. We also prove that locally approximately inner and uniformly outer \({\mathbb{Z}^2}\)-actions on a unital simple AF algebra with a unique trace have the Rohlin property and classify them up to cocycle conjugacy employing the OrderExt group as classification invariants.

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Authors and Affiliations

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

    Hiroki Matui

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  1. Hiroki Matui
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Correspondence to Hiroki Matui.

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Communicated by Y. Kawahigashi

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Matui, H. \({\mathbb{Z}}\)-Actions on AH Algebras and \({\mathbb{Z}^2}\)-Actions on AF Algebras. Commun. Math. Phys. 297, 529–551 (2010). https://doi.org/10.1007/s00220-009-0969-z

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  • DOI: https://doi.org/10.1007/s00220-009-0969-z

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