Generalized Derivations of BiHom-Lie Algebras

Abdelkader BH

Abstract

BiHom-Lie algebra is a generalized Hom-Lie algebra endowed with two commuting multiplicative linear maps. This paper is devoted to investigate the generalized derivation of BiHom-Lie algebra. We generalize the main results of Leger and Luks to the case of BiHom-Lie algebra. Firstly we review some concepts associated with BiHom-Lie algebra L. Furthermore, we give the definitions of the generalized derivation GDer(L), quasiderivations QDer(L), center derivation Z(L), centroid C(L) and quasicentroid QC(L). Later one, we give some useful proprieties and connections between these derivations. In particular, we prove that GDer(L)=QDer(L)+QC(L). We also prove that QDer(L) can be embedded as derivations in larger BiHom-Lie algebra.