Bernoullicity of lopsided principal algebraic actions

TL;DR

This paper proves that certain algebraic actions related to lopsided elements in the group ring are Bernoulli, under specific orderability conditions, extending understanding of their probabilistic properties.

Contribution

It establishes Bernoullicity for principal algebraic actions linked to lopsided elements in the integral group ring with orderability assumptions, a novel result in algebraic dynamics.

Findings

Principal algebraic actions are Bernoulli under given conditions.

Lopsided elements in the group ring lead to Bernoulli actions.

Orderability condition is crucial for the result.

Abstract

We show that the principal algebraic actions of countably infinite groups associated to lopsided elements in the integral group ring satisfying some orderability condition are Bernoulli.