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Minimal Dynamical Systems on the Product of the Cantor Set and the Circle

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Abstract

We prove that a crossed product algebra arising from a minimal dynamical system on the product of the Cantor set and the circle has real rank zero if and only if the set of invariant measures of the system come from the associated Cantor minimal system. In the case that cocycles take values in the rotation group, it is also shown that this condition implies tracial rank zero, and in particular, the crossed product algebra is isomorphic to a unital simple AT-algebra of real rank zero. Under the same assumption, we show that two systems are approximately K-conjugate if and only if there exists a sequence of isomorphisms between two associated crossed products which approximately maps

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, P.R. China

    Huaxin Lin

  2. Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan

    Hiroki Matui

  3. Department of Mathematics, University of Oregon, Eugene, OR, 97403, USA

    Huaxin Lin

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  1. Huaxin Lin
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  2. Hiroki Matui
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Correspondence to Huaxin Lin.

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Communicated by Y. Kawahigashi

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Lin, H., Matui, H. Minimal Dynamical Systems on the Product of the Cantor Set and the Circle. Commun. Math. Phys. 257, 425–471 (2005). https://doi.org/10.1007/s00220-005-1298-5

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  • DOI: https://doi.org/10.1007/s00220-005-1298-5

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