Isomorphism rigidity of irreducible algebraic ℤd-actions

被引：0

作者：

Bruce Kitchens

Klaus Schmidt

机构：

[1] Mathematical Sciences Department,

[2] IBM T.J. Watson Research Center,undefined

[3] Yorktown Heights,undefined

[4] NY 10598,undefined

[5] USA (e-mail: brucek@us.ibm.com),undefined

[6] Mathematics Institute,undefined

[7] University of Vienna,undefined

[8] Strudlhofgasse 4,undefined

[9] A-1090 Vienna,undefined

[10] Austria,undefined

[11] Erwin Schrödinger Institute for Mathematical Physics,undefined

[12] Boltzmanngasse 9,undefined

[13] A-1090 Vienna,undefined

[14] Austria (e-mail: klaus.schmidt@univie.ac.at),undefined

来源：

Inventiones mathematicae | 2000年 / 142卷

关键词：

Abelian Group; Invariant Measure; Prime Ideal; Haar Measure; Dual Module;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

An irreducible algebraic ℤd-actionα on a compact abelian group X is a ℤd-action by automorphisms of X such that every closed, α-invariant subgroup Y⊊X is finite. We prove the following result: if d≥2, then every measurable conjugacy between irreducible and mixing algebraic ℤd-actions on compact zero-dimensional abelian groups is affine. For irreducible, expansive and mixing algebraic ℤd-actions on compact connected abelian groups the analogous statement follows essentially from a result by Katok and Spatzier on invariant measures of such actions (cf. [4] and [3]). By combining these two theorems one obtains isomorphism rigidity of all irreducible, expansive and mixing algebraic ℤd-actions with d≥2.

引用

页码：559 / 577

页数：18