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Rokhlin extensions and lifting disjointness

Published online by Cambridge University Press:  23 September 2003

MARIUSZ LEMAŃCZYK  and
FRANÇOIS PARREAU
MARIUSZ LEMAŃCZYK
Affiliation:
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87–100 Toruń, Poland (e-mail: [email protected])
FRANÇOIS PARREAU
Affiliation:
Laboratoire d'Analyse, Géométrie et Applications, UMR 7539, Université Paris 13 et CNRS, 99, av. J.-B. Clément, 93430 Villetaneuse, France (e-mail: [email protected])
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Abstract

Assuming that two ergodic automorphisms T and R are disjoint, we prove that an ergodic extension $\tilde{T}$ of T remains disjoint with R when, in a representation of $\tilde{T}$ as a skew product over T, the fiber automorphisms belong to a mildly mixing action of a second countable locally countable abelian (LCA) group and the corresponding cocycle with values in this group is ergodic. This allows us to show that the class of ergodic automorphisms which are disjoint from all weakly mixing automorphisms is not closed under taking ergodic joinings, thereby solving a problem stated by E. Glasner and B. Weiss.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 5 , October 2003 , pp. 1525 - 1550
Copyright
2003 Cambridge University Press

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