Mixing Shifts of Finite Type with Non-Elementary Surjective Dimension Representations

The dimension representation has been a useful tool in studying the mysterious automorphism group of a shift of finite type, the classification of shifts of finite type, and surrounding problems. We discuss the importance of understanding the image of the dimension representation and discuss the candidate range for the fundamental case of mixing shifts of finite type. We present the first class of examples of mixing shifts of finite type for which the dimension representation is surjective necessarily using non-elementary conjugacies.