Harmonic Models and Bernoullicity

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.

40 pages, no figures. Significant changes to the proofs of results in Section 3. The methods now require additional results on tracial von Neumann algebras, which has been added to Appendix A. Comments welcome!