The main goal of this paper is to construct an “algebraic” representation of a group automorphisms Aut Γ for any elementary solvable group Γ. “Algebraic” means that the image of a semisimple (unipotent) automorphism, in the sense of Wang, will be a semisimple (unipotent) matrix Theorem 1. This gives an answer on the question asking by Wang. As a corollary of this theorem, we show that for any group of automorphisms Aut Γ of a lattice Γ in a solvable connected group Lie G there exist a representation ρ : Aut Γ → G L n (ℤ), such that ρ(Aut Γ) is an arithmetic subgroup in the Zariski closure .