Lie algebras with almost dimensionally nilpotent inner derivations Original Research Article

The structure of the Lie algebras with almost dimensionally nilpotent inner derivations is studied. It is proved that, if the base field is of characteristic 0, then, when d>6 is odd, there exist just two d-dimensional Lie algebras; when d>6 is even, there exists just one d-dimensional Lie algebra such that these Lie algebras are nonsolvable and have some almost dimensionally nilpotent inner derivations.