Bernoulli actions of sofic groups have completely positive entropy

被引：18
|
作者：
Kerr, David [1 ]
机构：
[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
来源：
ISRAEL JOURNAL OF MATHEMATICS | 2014年 / 202卷 / 01期
基金：
美国国家科学基金会;
关键词：
AMENABLE GROUP-ACTIONS; MALLEABLE ACTIONS; SUPERRIGIDITY; CONSTRUCTION;
D O I：
10.1007/s11856-014-1077-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that every Bernoulli action of a sofic group has completely positive entropy with respect to every sofic approximation net. We also prove that every Bernoulli action of a finitely generated free group has the property that each of its nontrivial factors with a finite generating partition has positive f-invariant.
引用
收藏
页码：461 / 474
页数：14
相关论文
共 50 条
  • [1] Bernoulli actions of sofic groups have completely positive entropy
    David Kerr
    [J]. Israel Journal of Mathematics, 2014, 202 : 461 - 474
  • [2] ENTROPY AND ACTIONS OF SOFIC GROUPS
    Weiss, Benjamin
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (10): : 3375 - 3383
  • [3] UNIFORM MIXING AND COMPLETELY POSITIVE SOFIC ENTROPY
    Austin, Tim
    Burton, Peter
    [J]. JOURNAL D ANALYSE MATHEMATIQUE, 2019, 138 (02): : 597 - 612
  • [4] Uniform mixing and completely positive sofic entropy
    Tim Austin
    Peter Burton
    [J]. Journal d'Analyse Mathématique, 2019, 138 : 597 - 612
  • [5] Entropy and the variational principle for actions of sofic groups
    David Kerr
    Hanfeng Li
    [J]. Inventiones mathematicae, 2011, 186 : 501 - 558
  • [6] Entropy and the variational principle for actions of sofic groups
    Kerr, David
    Li, Hanfeng
    [J]. INVENTIONES MATHEMATICAE, 2011, 186 (03) : 501 - 558
  • [7] The spectrum of completely positive entropy actions of countable amenable groups
    Dooley, AH
    Golodets, VY
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2002, 196 (01) : 1 - 18
  • [8] POSITIVE ENTROPY ACTIONS OF COUNTABLE GROUPS FACTOR ONTO BERNOULLI SHIFTS
    Seward, Brandon
    [J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 33 (01) : 57 - 101
  • [9] Non-Bernoulli systems with completely positive entropy
    Dooley, A. H.
    Golodets, V. Ya.
    Rudolph, D. J.
    Sinel'shchikov, S. D.
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2008, 28 : 87 - 124
  • [10] Sofic entropy of Gaussian actions
    Hayes, Ben
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2017, 37 : 2187 - 2222
12345