Derivations of two-step nilpotent algebras

In this paper we study the Lie algebras of derivations of two-step nilpotent algebras. We obtain a class of Lie algebras with trivial center and abelian ideal of inner derivations. Among these, the relations between the complex and the real case of the indecomposable Heisenberg Leibniz algebras are thoroughly described. Finally we show that every almost inner derivation of a complex nilpotent Leibniz algebra with one-dimensional commutator ideal, with three exceptions, is an inner derivation.

Automated summary

This paper investigates the Lie algebras of derivations in two-step nilpotent algebras. A class of Lie algebras with trivial center and abelian ideal of inner derivations is obtained. The relations between the complex and real cases of the indecomposable Heisenberg Leibniz algebras are thoroughly described. Finally, it is shown that almost every inner derivation of a complex nilpotent Leibniz algebra with a one-dimensional commutator ideal is an inner derivation, except for three exceptions.