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：
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
收藏
页码：2460 / 2471
页数：12
相关论文
共 50 条
  • [21] An Infinite Hierarchy of Language Families Resulting from Stateless Pushdown Automata with Limited Pushdown Alphabets
    Meduna, Alexander
    Vrabel, Lukas
    Zemek, Petr
    DESCRIPTIONAL COMPLEXITY OF FORMAL SYSTEMS, DCFS 2012, 2012, 7386 : 236 - 243
  • [22] A generalization of amenability and inner amenability of groups
    Ali Ghaffari
    Czechoslovak Mathematical Journal, 2012, 62 : 729 - 742
  • [23] Amenability and acyclicity in bounded cohomology
    Moraschini, Marco
    Raptis, George
    REVISTA MATEMATICA IBEROAMERICANA, 2023, 39 (06) : 2371 - 2404
  • [24] A generalization of amenability and inner amenability of groups
    Ghaffari, Ali
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2012, 62 (03) : 729 - 742
  • [25] Bounded model checking of infinite state systems: Exploiting the automata hierarchy
    Schuele, T
    Schneider, K
    SECOND ACM AND IEEE INTERNATIONAL CONFERENCE ON FORMAL METHODS AND MODELS FOR CO-DESIGN, PROCEEDINGS, 2004, : 17 - 26
  • [26] AUTOMATONS WITH STACKS ON INFINITE ALPHABETS
    IDT, J
    LECTURE NOTES IN COMPUTER SCIENCE, 1984, 166 : 260 - 273
  • [27] LANGUAGES OVER INFINITE ALPHABETS
    AUTEBERT, JM
    BEAUQUIER, J
    BOASSON, L
    DISCRETE APPLIED MATHEMATICS, 1980, 2 (01) : 1 - 20
  • [28] Coding on Countably Infinite Alphabets
    Boucheron, Stephane
    Garivier, Aurelien
    Gassiat, Elisabeth
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2009, 55 (01) : 358 - 373
  • [29] Bounded and semibounded representations of infinite dimensional Lie groups
    Neeb, Karl-Hermann
    REPRESENTATION THEORY - CURRENT TRENDS AND PERSPECTIVES, 2017, : 541 - +
  • [30] On finite alphabets and infinite bases
    Chen, Taolue
    Fokkink, Wan
    Luttik, Bas
    Nain, Sumit
    INFORMATION AND COMPUTATION, 2008, 206 (05) : 492 - 519
12345