可数sofic群的等距线性作用的维数

荣祯

数学学报 ›› 2020, Vol. 63 ›› Issue (5) : 465-488.

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数学学报 ›› 2020, Vol. 63 ›› Issue (5) : 465-488. DOI: 10.12386/A2020sxxb0039
论文

可数sofic群的等距线性作用的维数

    荣祯
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Dimension for Isometric Linear Actions of Countable Sofic Groups

    Zhen RONG
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摘要

我们对复Banach空间上的可数sofic群的等距线性作用提出了一种新的维数,推广了复Banach空间上的可数顺从群的等距线性作用的Voiculescu维数,并且在可数sofic群的情形回答了Gromov的一个问题.

Abstract

We introduce a new dimension for isometric linear actions of countable sofic groups on complex Banach spaces. This generalizes the Voiculescu dimension for isometric linear actions of countable amenable groups on complex Banach spaces, and answers a question of Gromov in the case of countable sofic groups.

关键词

sofic群 / 顺从群 / Voiculescu维数

Key words

sofic group / amenable group / Voiculescu dimension

引用本文

导出引用
荣祯. 可数sofic群的等距线性作用的维数. 数学学报, 2020, 63(5): 465-488 https://doi.org/10.12386/A2020sxxb0039
Zhen RONG. Dimension for Isometric Linear Actions of Countable Sofic Groups. Acta Mathematica Sinica, Chinese Series, 2020, 63(5): 465-488 https://doi.org/10.12386/A2020sxxb0039

参考文献

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