Generalized derivations of Z2×Z2-graded Lie algebras

Let g be a Z2×Z2-graded Lie algebra over a field of characteristic ≠2. This paper deals with the study of various important properties of derivation subalgebra Der(g), generalized derivation subalgebra Gder(g), quasiderivation subalgebra Qder(g) of a Z2×Z2-graded Lie algebra g, satisfying the inclusion relation Der(g)⊆Qder(g)⊆Gder(g)⊆Hom(g,g). The paper contains a complete characterization of Z2×Z2-graded Lie algebras g which satisfy Qder(g)=Hom(g,g). It also proves that the quasiderivations of a Z2×Z2-graded Lie algebra can be embedded as derivations in a larger Z2×Z2-graded Lie algebra.