New Examples of Bernoulli Algebraic Actions

Abstract

We give examples of principal algebraic actions of the noncommutative free group $F$ 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 $F$.

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

References in corpus (2)

• Examples in the entropy theory of countable group actions
• Max-Min theorems for weak containment, square summable homoclinic points, and completely positive entropy