Classification of Solvable Lie Algebras

Abstract

In this paper we describe a simple method for obtaining a classification of small-dimensional solvable Lie algebras. Using this method, we obtain the classification of three- and fourdimensional solvable Lie algebras (over fields of any characteristic). Precise conditions for isomorphism are given.

Keywords:

• Primary 17B03, 17-08
• Lie algebras
• classification
• Gröbner bases