BiHom-Lie colour algebras structures

Abstract: BiHom-Lie Colour algebra is a generalized Hom-Lie Colour algebra endowed with two commuting multiplicative linear maps. The main purpose of this paper is to define representations and a cohomology of BiHom-Lie colour algebras and to study some key constructions and properties. Moreover, we discuss $\alpha^{k}\beta^l$-generalized derivations, $\alpha^{k}\beta^l$-quasi-derivations and $\alpha^{k}\beta^l$-quasi-centroid. We provide some properties and their relationships with BiHom-Jordan colour algebra.