Minimal models for actions of amenable groups

被引：3

作者：

Frej, Bartosz ^{[1
]}

Huczek, Dawid ^{[1
]}

机构：

[1] Wroclaw Univ Sci & Technol, Fac Pure & Appl Math, Wybrzeze Wyspianskiego 27, PL-50370 Wroclaw, Poland

来源：

GROUPS GEOMETRY AND DYNAMICS | 2017年 / 11卷 / 02期

关键词：

Topologicalmodel; dynamical system; group action; amenable group; invariant measure; Choquet simplex; Borel isomorphism;

D O I：

10.4171/GGD/408

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that on a metrizable, compact, zero-dimensional space every free action of an amenable group is measurably isomorphic to a minimal G-action with the same, i.e. affinely homeomorphic, simplex of measures.

引用

页码：567 / 583

页数：17

共 50 条

[1] AMENABLE ACTIONS OF GROUPS
ADAMS, S
ELLIOTT, GA
GIORDANO, T
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 344 (02) : 803 - 822
[2] Rigid actions of amenable groups
Samet, Iddo
ISRAEL JOURNAL OF MATHEMATICS, 2009, 173 (01) : 61 - 90
[3] Amenable actions of nonamenable groups
Grigorchuk R.
Nekrashevych V.
Journal of Mathematical Sciences, 2007, 140 (3) : 391 - 397
[4] Rigid actions of amenable groups
Iddo Samet
Israel Journal of Mathematics, 2009, 173 : 61 - 90
[5] Amenable minimal Cantor systems of free groups arising from diagonal actions
Suzuki, Yuhei
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2017, 722 : 183 - 214
[6] Amenable actions and exactness for discrete groups
Ozawa, N
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 330 (08): : 691 - 695
[7] Ergodic amenable actions of algebraic groups
Raja, CRE
GLASGOW MATHEMATICAL JOURNAL, 2004, 46 : 97 - 100
[8] AMENABLE ACTIONS OF DISCRETE-GROUPS
ELLIOTT, GA
GIORDANO, T
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1993, 13 : 289 - 318
[9] Bowen entropy for actions of amenable groups
Zheng, Dongmei
Chen, Ercai
ISRAEL JOURNAL OF MATHEMATICS, 2016, 212 (02) : 895 - 911
[10] Bowen entropy for actions of amenable groups
Dongmei Zheng
Ercai Chen
Israel Journal of Mathematics, 2016, 212 : 895 - 911

← 1 2 3 4 5 →