Classification of Finite-Dimensional Lie Algebras with Respect to the Length of Their Chief Series

Abstract

In this paper, we study finite dimensional Lie algebras with respect to the length of their chief series. We examine separately the semisimple, solvable, and mixed cases over fields of characteristic zero, and we establish several structural results describing Lie algebras of prescribed chief length. In the solvable and mixed settings, the problem is reduced to the study of irreducible modules arising from suitable quotient actions. In positive characteristic, we investigate semisimple Lie algebras by means of Block s structural theorem and obtain several results concerning Lie algebras of chief length two.