New Examples of Bernoulli Algebraic Actions
Abstract
We give examples of principal algebraic actions of the noncommutative free group of rank two, as well as other groups, by automorphisms of a connected compact abelian group for which there is an explicit measurable isomorphism to a Bernoulli action of the group. The isomorphism is defined using homoclinic points, a method that has been used earlier to construct symbolic covers of algebraic actions. To our knowledge, these are the first nontrivial examples of the Bernoullicity of an algebraic action of .
Cite
@article{arxiv.1905.09966,
title = {New Examples of Bernoulli Algebraic Actions},
author = {Douglas Lind and Klaus Schmidt},
journal= {arXiv preprint arXiv:1905.09966},
year = {2021}
}
Comments
13 pages. This update to our previous version generalizes our arguments to more acting groups and a more general class of principal actions. It also includes a different proof that the Bernoulli measure maps to Haar measure using a Fourier coefficient argument due to Ben Hayes