Isomorphism rigidity of commuting automorphisms

Abstract

Abstract. Let d > 1, and let (X, α) and (Y, β) be two zero-entropy Z d -actions on compact abelian groups by d commuting automorphisms. We show that if all lower rank subactions of α and β have completely positive entropy, then any measurable equivariant map from X to Y is an affine map. In particular, two such actions are measurably conjugate if and only if they are algebraically conjugate.