An example of compact extensions of Kronecker factors and skew products of irrational rotations with finite groups
type: Item
instance of: scholarly article
title: An example of compact extensions of Kronecker factors and skew products of irrational rotations with finite groups
zbMATH Open document ID: 0841.28014
DOI: 10.1007/BF02762080
author: Yanyan Li
published in: Israel Journal of Mathematics
publication date: 1996-07-18T00:00:00Z
review text: Let \(S\) and \(T\) be commuting ergodic measure preserving transformations on a probability space \((X, {\mathcal B}, \mu)\). The Kronecker factor \(K_1(T)\) is a \(T\)-invariant sub \(\sigma\)-algebra of \(\mathcal B\), and may be thought of as the maximal discrete spectrum factor of \(T\). It is known that \(ST= TS\) implies \(K_1(T)= K_1(S)\). The purpose of this paper is to study certain compact extensions of the Kronecker factor, called the degree 2 Kronecker factor \(K_2(T)\), and show that they can be different for two commuting ergodic automorphisms. The examples used are finite skew products of rotations. Some new criteria for the ergodicity of such maps are given.
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 836165
zbMATH Keywords: ergodic measure preserving transformations
zbMATH Keywords: Kronecker factor
zbMATH Keywords: compact extensions
zbMATH Keywords: skew products
reviewed by: Geoffrey R. Goodson
MaRDI profile type: Publication
cites work: Q3909268
cites work: Sequence Entropy Relative to an Invariant σ-Algebra
cites work: Sigma-finite invariant measures for smooth mappings of the circle
cites work: Q5727753
cites work: Q4767350
cites work: Ergodicity of cylinder flows arising from irregularities of distribution
cites work: Q5336415
cites work: Finite group extensions of irrational rotations
cites work: Q3931654
cites work: Extensions of ergodic group actions
description: scientific article; zbMATH DE number 836165