RELATIVE ENTROPY DIMENSION FOR COUNTABLE AMENABLE GROUP ACTIONS*

doi:10.1007/s10473-023-0607-4

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (6): 2430-2448.doi: 10.1007/s10473-023-0607-4

RELATIVE ENTROPY DIMENSION FOR COUNTABLE AMENABLE GROUP ACTIONS^*

Zubiao XIAO¹, Zhengyu YIN^2,†

1. School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, China;
2. Department of Mathematics, Nanjing University, Nanjing 210093, China

收稿日期:2022-06-07 修回日期:2023-05-29 发布日期:2023-12-08
通讯作者: †Zhengyu YIN, E-mail: yzy_nju_20@163.com
作者简介:Zubiao XIAO , E-mail: xzb2020@fzu.edu.cn
基金资助:
The research was supported by the NNSF of China (12201120, 12171233) and the Educational Research Project for Young and Middle-aged Teachers of Fujian Province (JAT200045).

RELATIVE ENTROPY DIMENSION FOR COUNTABLE AMENABLE GROUP ACTIONS^*

Zubiao XIAO¹, Zhengyu YIN^2,†

1. School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, China;
2. Department of Mathematics, Nanjing University, Nanjing 210093, China

Received:2022-06-07 Revised:2023-05-29 Published:2023-12-08
Contact: †Zhengyu YIN, E-mail: yzy_nju_20@163.com
About author:Zubiao XIAO , E-mail: xzb2020@fzu.edu.cn
Supported by:
The research was supported by the NNSF of China (12201120, 12171233) and the Educational Research Project for Young and Middle-aged Teachers of Fujian Province (JAT200045).

摘要/Abstract

摘要： We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups. First, for a given Følner sequence $\{F_n\}_{n=0}^{+\infty}$, we define the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity. we also investigate the relations among these. Second, we introduce the notion of a relative dimension set. Moreover, using the method, we discuss the disjointness between the relative entropy zero extensions via the relative dimension sets of two extensions, which says that if the relative dimension sets of two extensions are different, then the extensions are disjoint.

关键词: amenable groups, relative entropy dimensions, relative dimension sets

Abstract: We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups. First, for a given Følner sequence $\{F_n\}_{n=0}^{+\infty}$, we define the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity. we also investigate the relations among these. Second, we introduce the notion of a relative dimension set. Moreover, using the method, we discuss the disjointness between the relative entropy zero extensions via the relative dimension sets of two extensions, which says that if the relative dimension sets of two extensions are different, then the extensions are disjoint.

Key words: amenable groups, relative entropy dimensions, relative dimension sets

中图分类号:

37B99

Zubiao XIAO, Zhengyu YIN. RELATIVE ENTROPY DIMENSION FOR COUNTABLE AMENABLE GROUP ACTIONS^*[J]. 数学物理学报(英文版), 2023, 43(6): 2430-2448.

Zubiao XIAO, Zhengyu YIN. RELATIVE ENTROPY DIMENSION FOR COUNTABLE AMENABLE GROUP ACTIONS^*[J]. Acta mathematica scientia,Series B, 2023, 43(6): 2430-2448.

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RELATIVE ENTROPY DIMENSION FOR COUNTABLE AMENABLE GROUP ACTIONS^*

RELATIVE ENTROPY DIMENSION FOR COUNTABLE AMENABLE GROUP ACTIONS^*

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