Rank One And Loosely Bernoulli Actions In Zᵈ

Aimee S. A. Johnson, Swarthmore College
A. A. Sahin

Abstract

We define rank one for Zᵈ actions and show that those rank one actions with a certain tower shape are loosely Bernoulli for d greater than or equal to 1. We also construct a zero entropy Z² loosely Bernoulli action with a zero entropy, ergodic, non-loosely Bernoulli one-dimensional subaction.