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 admitting a periodic generalized derivation D Der(-1,1,1)(). © 2020 World Scientific Publishing Company.

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