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Twisted Group C*-Algebras as Compact Quantum Metric Spaces

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Abstract

We construct a class of compact quantum metric spaces. We prove that twisted reduced group C*-algebras for discrete groups with twisted rapid decay property are compact quantum metric spaces, which contain noncommutative tori, hyperbolic reduced group C*-algebras and discrete Heisenberg group C*-algebras, and that the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, 200241, China

    Botao Long

  2. Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China

    Wei Wu

Authors
  1. Botao Long
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  2. Wei Wu
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Correspondence to Wei Wu.

Additional information

The research was supported by National Natural Science Foundation of China (Grant No. 11171109), and by Science and Technology Commission of Shanghai Municipality (Grant No. 13dz2260400).

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Long, B., Wu, W. Twisted Group C*-Algebras as Compact Quantum Metric Spaces. Results Math 71, 911–931 (2017). https://doi.org/10.1007/s00025-016-0562-7

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  • DOI: https://doi.org/10.1007/s00025-016-0562-7

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