Amenability of bounded automata groups on infinite alphabets

被引：0

作者：

Reinke, Bernhard ^{[1
,2
,3
]}

机构：

[1] Aix Marseille Univ, Inst Math Marseille, UMR 7373, 163 Ave Luminy Case 901, F-13009 Marseille, France

[2] CRNS, 163 Ave Luminy Case 901, F-13009 Marseille, France

[3] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2024年 / 56卷 / 07期

基金：

欧洲研究理事会;

关键词：

LIOUVILLE; OPERATORS;

D O I：

10.1112/blms.13065

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the action of groups generated by bounded activity automata with infinite alphabets on their orbital Schreier graphs. We introduce an amenability criterion for such groups based on the recurrence of the first-level action. This criterion is a natural extension of the result that all groups generated by bounded activity automata with finite alphabets are amenable. Our motivation comes from the investigation of iterated monodromy groups of entire transcendental functions in holomorphic dynamics.

引用

页码：2460 / 2471

页数：12

共 18 条

[1] Amenability of linear-activity automaton groups [J].