In this paper we present a complete description of Lie algebras admitting an expanding and/or a hyperbolic automorphism in terms of ℝ-gradings of these Lie algebras. Using this, we then show that any infra-nilmanifold which admits an expanding map or an Anosov diffeomorphism also has a complete, affinely flat structure. © 2002 Elsevier Science B.V. All rights reserved.
Dekimpe, K., & Lee, K. B. (2003). Expanding maps, Anosov diffeomorphisms and affine structures on infra-nilmanifolds. Topology and Its Applications, 130(3), 259–269. https://doi.org/10.1016/S0166-8641(02)00224-9