Almost inner derivations of Lie algebras II

We continue the algebraic study of almost inner derivations of Lie algebras over a field of characteristic zero and determine these derivations for free nilpotent Lie algebras, for almost abelian Lie algebras, for Lie algebras whose solvable radical is abelian and for several classes of filiform nilpotent Lie algebras. We find a family of [Formula: see text]-dimensional characteristically nilpotent filiform Lie algebras [Formula: see text], for all [Formula: see text], all of whose derivations are almost inner. Finally, we compare the almost inner derivations of Lie algebras considered over two different fields [Formula: see text] for a finite-dimensional field extension.

Almost Inner Derivations of Some Nilpotent Leibniz Algebras

We investigate almost inner derivations of some finite-dimensional nilpotent Leibniz algebras. We show the existence of almost inner derivations of Leibniz filiform non-Lie algebras differing from inner derivations, we also show that the almost inner derivations of some filiform Leibniz algebras containing filiform Lie algebras do not coincide with inner derivations