Classification of nilpotent lie algebras of dimension nine whose maximum abelian ideal is of dimension seven

Abstract

The classification of Nilpotent Lie Algebras has been partially achieved up to dimension eight but this specific problem remained unsolved, since it required an enormous amount of calculations. Nowadays, with the aid of modern computers, it can be solved by designing the proper algorithms. The aim of this paper is to provide the results of the classification of Nilpotent Lie Algebras of dimension nine, whose maximum abelian ideal is of dimension seven.

Keywords:

• Solvable
• Nilpotent algebras
• algebraic manipulation
• classification of Nilpotent Lie Algebras
• dimension nine
• abelian ideal and the classification problem

M.O.S. (A.M.S):

• 17B30

C.R. Categories:

• G.4