Generalized Derivations Of N-Hom-Leibniz Algebras

As a result of the dual needs of Lie algebras and physics,people began to study Hom-Lie algebras,and as a general case of Hom-Lie algebras,the structures and properties of Hom-Leibniz algebras are also widely studied.In this paper,we generalize the concepts of the generalized derivation algebra GDer(V),quasi-derivation algebra QDer(V),central derivation algebra ZDer(V),centroid C(V)and quasi-centroid QC(V)of finite dimensional Hom-Leibniz algebras over the field F characterized by 0.The basic properties of derivation algebra of n-Hom-Leibniz algebras and their relations are studied,then we obtain that the derivation algebra,generalized derivation algebra,quasi-derivation algebra and centroid of n-Hom-Leibniz algebra are all the Hom-subalgebras of the Hom-Lie algebra((?),[·,·],α),and that the central derivation algebra of n-Hom-Leibniz alge-bras is its Hom-ideal of derivative algebras.We also get a conclusion that[C(V),QC(V)](?)End(V,Z(V)),when n-Hom-Leibniz algebra(V,[·,…,·],α)is multiplicative and α is surjective.