Determination of 7-Dimensional Indecomposable Nilpotent Complex Lie Algebras by Adjoining a Derivation to 6-Dimensional Lie Algebras

Abstract

For any complex 6-dimensional nilpotent Lie algebra \(\mathfrak{g},\) we compute the strain of all indecomposable 7-dimensional nilpotent Lie algebras which contain \(\mathfrak{g}\) by the adjoining a derivation method. We get a new determination of all 7-dimensional complex nilpotent Lie algebras, allowing to check earlier results (some contain errors), along with a cross table intertwining nilpotent 6- and 7-dimensional Lie algebras.