Generalized Derivations of BiHom-Lie AlgebrasAbdelkader BH*
Université de Sfax, Faculté des Sciences Sfax, BP 1171, 3038 Sfax, Tunisia
- *Corresponding Author:
- Abdelkader BH
Université de Sfax
Faculté des Sciences Sfax
BP 1171, 3038 Sfax, Tunisia
E-mail: [email protected]
Received Date: December 12, 2017; Accepted Date: February 11, 2017; Published Date: February 28, 2017
Citation: Abdelkader BH (2017) Generalized Derivations of BiHom-Lie Algebras. J Generalized Lie Theory Appl 11:259. doi:10.4172/1736-4337.1000259
Copyright: © 2017 Abdelkader BH. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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.