Mathematica Eterna
Open Access

Abstract

Generalized derivations of n-Hom Lie superalgebras

Jinsen Zhou and Guangzhe Fan

It is well known that n-Hom Lie superalgebras are certain generalizations of n-Lie algebras. This paper is devoted to investigate the generalized derivations of multiplicative n-Hom Lie superalgebras. We generalize the main results of Leger and Luks to the case of multiplicative n-Hom Lie superalgebras. Firstly, we review some concepts associated with a multiplicative n-Hom Lie superalgebra N. Furthermore, we give the definitions of the generalized derivations, quasiderivations, center derivations, centroids and quasicentroids. Obviously, we have the following tower ZDer(N) ⊆ Der(N) ⊆ QDer(N) ⊆ GDer(N) ⊆ End(N). Later on, we give some useful properties and connections between these derivations. Moreover, we obtain that the quasiderivation of N can be embedded as a derivation in a larger multiplicative n-Hom Lie superalgebra. Finally, we conclude that the derivation of the larger multiplicative n-Hom Lie superalgebra has a direct sum decomposition when the center of N is equal to zero.