Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals

Abstract

By combining basic techniques in Lie Theory and a computer algebra tool which is the so-called triangular decomposition, the class of 7-dimensional real and complex indecomposable solvable Lie algebras having 5-dimensional nilradicals is classified up to isomorphism. In association with Gong (1998), Parry (2007), Hindeleh and Thompson (2008), we achieve a full classification of 7-dimensional real and complex indecomposable solvable Lie algebras.

Keywords:

• Lie algebra
• nilradical

2020 Mathematics Subject Classification:

• 15A21
• 16G60
• 17B30
• 20G05

Additional information

Funding

This research is supported by the project SPD2019.01.37.