Rigidity of the measurable structure for algebraic actions of higher-rank Abelian groups

Boris Kalinin; Ralf Spatzier

doi:10.1017/S014338570400046X

Rigidity of the measurable structure for algebraic actions of higher-rank Abelian groups

Boris Kalinin, Ralf Spatzier

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We investigate rigidity of measurable structure for higher-rank Abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a zero entropy measure with Haar measures along the leaves. We deduce various rigidity theorems for isomorphisms and joinings as corollaries.

Original language	English (US)
Pages (from-to)	175-200
Number of pages	26
Journal	Ergodic Theory and Dynamical Systems
Volume	25
Issue number	1
DOIs	https://doi.org/10.1017/S014338570400046X
State	Published - Feb 2005

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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abstract = "We investigate rigidity of measurable structure for higher-rank Abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a zero entropy measure with Haar measures along the leaves. We deduce various rigidity theorems for isomorphisms and joinings as corollaries.",

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Rigidity of the measurable structure for algebraic actions of higher-rank Abelian groups

Abstract

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