New special Einstein pseudo-Riemannian metrics on solvable Lie algebras

We exhibit a concrete procedure to construct Einstein pseudo-Kahler and para-Kahler metrics on solvable Lie algebras. We apply this method to classify all the rank-one pseudo-Iwasawa extensions of type-(Nil4) nilsoliton in low dimension. We prove that such metrics exist on the rank-one pseudo-Iwasawa extension of the generalized Heisenberg Lie algebra. Further ideas and suggestions to produce more special Einstein pseudoRiemannian metrics arc exposed.