  The classification of all real and rational Anosov Lie algebras up to
dimension 8 is given by Lauret and Will. In this paper we study 9-dimensional
Anosov Lie algebras by using the properties of very special algebraic numbers
and Lie algebra classification tools. We prove that there exists a unique (up
to a Lie algebra isomorphism) complex 3-step Anosov Lie algebra of dimension 9.
In the 2-step case, we prove that a 2-step real 9-dimensional Anosov Lie
algebra with no abelian factor must have a 3-dimensional derived algebra and we
characterize these Lie algebras in terms of their Pfaffian forms. Among these
Lie algebras, we have found a family of infinitely many complex nonisomorphic
Anosov Lie algebras.
