Classification of Lie Subalgebras up to an Inner Automorphism

Abstract

In this paper, a useful classification of all Lie subalgebras of a given Lie algebraup to an inner automorphism is presented. This method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. After main results, we have applied this procedure for classifying the Lie subalgebras of some examples of Lie algebras.

Keywords

• Lie algebra
• vector fields
• optimal system