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The tracial topological rank of certain C*-algebras

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Abstract

Let 0 → I → A → A/I → 0 be a short exact sequence of C*-algebras with A unital. Suppose that I has tracial topological rank no more than one and A/I belongs to a class of certain C*-algebras. We show that A has tracial topological rank no more than one if the extension is quasidiagonal, and A has the property (P 1) if the extension is tracially quasidiagonal.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, 200092, China

    XiaoChun Fang & YiLe Zhao

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  1. XiaoChun Fang
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  2. YiLe Zhao
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Correspondence to XiaoChun Fang.

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Dedicated to Professor Richard V. Kadison on the Occasion of his 85th Birthday

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Fang, X., Zhao, Y. The tracial topological rank of certain C*-algebras. Sci. China Math. 54, 2295–2307 (2011). https://doi.org/10.1007/s11425-011-4251-4

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  • DOI: https://doi.org/10.1007/s11425-011-4251-4

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