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New examples of Bernoulli algebraic actions
Published online by Cambridge University Press: 17 May 2021
Abstract
We give an example of a principal algebraic action of the non-commutative free group
${\mathbb {F}}$
of rank two by automorphisms of a connected compact abelian group for which there is an explicit measurable isomorphism with the full Bernoulli 3-shift action of
${\mathbb {F}}$
. The isomorphism is defined using homoclinic points, a method that has been used to construct symbolic covers of algebraic actions. To our knowledge, this is the first example of a Bernoulli algebraic action of
${\mathbb {F}}$
without an obvious independent generator. Our methods can be generalized to a large class of acting groups.
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- Original Article
- Information
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
References
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