Generalized derivations of ω-Lie algebras

This paper explores the structure theory of compatible generalized derivations of finite-dimensional [Formula: see text]-Lie algebras over a field [Formula: see text]. We prove that any compatible quasiderivation of an [Formula: see text]-Lie algebra can be embedded as a compatible derivation into a larger [Formula: see text]-Lie algebra, refining the general result established by Leger and Luks [Generalized derivations of Lie algebras, J. Algebra 228(1) (2000) 165–203] for finite-dimensional nonassociative algebras. We also provide an approach to explicitly compute (compatible) generalized derivations and quasiderivations for all [Formula: see text]-dimensional non-Lie complex [Formula: see text]-Lie algebras.