Generalized derivations and some structure theorems for Lie algebras.

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 𝔤 admitting a periodic generalized derivation D ∈ Der (− 1 , 1 , 1) (𝔤). [ABSTRACT FROM AUTHOR]