A note on solvable and nilpotent Lie algebras

Abstract

Lie algebra L is called solvable if its derived series terminates in the zero subalgebra and also it is nilpotent if the lower central series become zero eventually. In this paper we will review the concepts and definitions of solvable and nilpotent Lie algebras and then describe some important conditions that finite dimensional lie algebras of characteristic zero are nilpotent and solvable.