Algorithmic construction of solvable rigid Lie algebras determined by generating functions

We introduce the notion of saturation of a nilradical with respect to the eigenvalue spectrum of a maximal torus of derivations and show the existence of a generating function and a factor sequence that completely determine the nilradical. As an application, a cohomologically rigid series of solvable Lie algebras of rank one with saturated nilradical is obtained for any and dimensions , where the eigenvalues of the torus are given by the sequence . An algorithmic procedure to search cohomologically rigid Lie algebras is proposed, based on the imposition of certain constraints on the generating function.