# Harmonic Models and Bernoullicity

## TL;DR

This paper explores algebraic actions as factors of Bernoulli shifts, providing examples involving harmonic models over certain groups, and discusses conditions under which these actions are Bernoulli.

## Contribution

It introduces new classes of algebraic actions that are factors of Bernoulli shifts, especially over left orderable groups, expanding understanding of Bernoulli properties.

## Key findings

- Examples of algebraic actions as factors of Bernoulli shifts.
- Identification of harmonic models over groups with large enough growth.
- Demonstration of Bernoulli actions without obvious Bernoulli partitions.

## Abstract

We give many examples of algebraic actions which are factors of Bernoulli shifts. These include certain harmonic models over left orderable groups of large enough growth, as well as algebraic actions associated to certain lopsided elements in any left orderable group. For many of our examples, the acting group is amenable so these actions are Bernoulli (and not just a factor of a Bernoulli), but there is no obvious Bernoulli partition.