Сentral and abelian extensions of solvable Lie and Leibniz algebras with filiform nilradical

This dissertation investigates the classification and structural properties of finite-dimensional solvable Lie and Leibniz algebras whose nilradicals are filiform. The research develops generalized central and abelian extension methods to describe solvable algebras, including one-dimensional extensions of solvable Lie algebras and abelian extensions of solvable Leibniz algebras. The scientific novelty of the work includes the classification of all one-dimensional central extensions of naturally graded filiform Lie algebras, the description of solvable Lie algebras with filiform nilradicals, and the development of a constructive method for abelian extensions of solvable Leibniz algebras. Furthermore, a complete characterization of the central extensions and deformations of the n-th Schrödinger algebra is presented.