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.

27 pages. arXiv admin note: text overlap with arXiv:1307.2612; text overlap with arXiv:1005.1127 by other authors

References in corpus (6)

• Representations of hom-Lie algebras
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Generalized derivations of (color) n-ary algebras
• Representations of Bihom-Lie algebras
• Generalized derivations of multiplicative $n$-ary Hom-$\Omega$ color algebras
• BiHom-Lie superalgebra structures

Cited by in corpus (8)

• The construction and deformation of BiHom-Novikov agebras
• Construtions and bimodules of BiHom-alternative and BiHom-Jordan algebras
• BiHom-Poisson color algebras
• On split regular BiHom-Poisson superalgebras
• On BiHom-analogue of generalized Lie algebras
• (Bi)Hom-Leibniz algebras
• Product and complex structures on 3-Bihom-Lie algebras
• The construction of 3-Bihom-Lie algebras