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Mean dimension and a non-embeddable example for amenable group actions

Volume 257 / 2022

Lei Jin, Kyewon Koh Park, Yixiao Qiao Fundamenta Mathematicae 257 (2022), 19-38 MSC: 37B05, 54F45. DOI: 10.4064/fm921-1-2021 Published online: 29 November 2021

Abstract

For every infinite (countable discrete) amenable group $G$ and every positive integer $d$ we construct a minimal $G$-action of mean dimension $d/2$ which cannot be embedded in the full $G$-shift on $([0,1]^d)^G$.

Authors

  • Lei JinCentro de Modelamiento Matemático
    Universidad de Chile
    and
    UMI 2807 – CNRS
    Beauchef 851
    Santiago, Chile
    e-mail
  • Kyewon Koh ParkKorea Institute for Advanced Study
    85 Hoegiro, Dongdaemun-gu
    Seoul 02455, Korea
    e-mail
  • Yixiao QiaoSchool of Mathematical Sciences
    South China Normal University
    Guangzhou 510631, China
    e-mail

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