Generalized derivations and some structure theorems for Lie algebras

Abstract

In this work, we show that the existence of invertible generalized derivations impose strong restrictions on the structure of a complex finite-dimensional Lie algebra. In particular, we recover the fact that a real Lie algebra admitting an abelian complex structure is necessarily solvable. On the other hand, we state a structure theorem for a Lie algebra [Formula: see text] admitting a periodic generalized derivation [Formula: see text].