  We study nilmanifolds admitting Anosov automorphisms by applying elementary
properties of algebraic units in number fields to the associated Anosov Lie
algebras. We identify obstructions to the existence of Anosov Lie algebras. The
case of 13-dimensional Anosov Lie algebras is worked out as an illustration of
the technique. Also, we recapture the following known results: (i) Every
7-dimensional Anosov nilmanifold is toral, and (ii) every 8-dimensional Anosov
Lie algebra with 3 or 5-dimensional derived algebra contains an abelian factor.
