Pseudo-algebraic Ricci solitons on Einstein nilradicals

We develop a variational method to find pseudo-algebraic Ricci solitons on connected Lie groups. As applications, we prove that every Einstein nilradical admits a non-Riemannian algebraic Ricci soliton, and that any algebraic Ricci soliton on a semi-simple Lie group is Einstein. Furthermore, we construct several Lorentz algebraic Ricci solitons on the nilpotent Lie groups which have a codimension one abelian ideal.