Representations of Bihom-Lie algebras

Abstract

Bihom-Lie algebra is a generalized Hom-Lie algebra endowed with two commuting multiplicative linear maps. In this paper, we study cohomology and representations of Bihom-Lie algebras. In particular, derivations, central extensions, derivation extensions, the trivial representation and the adjoint representation of Bihom-Lie algebras are studied in detail.

arXiv comment26 pages. arXiv admin note: text overlap with arXiv:1005.0140, arXiv:1405.2662 by other authors

References in corpus (4)

• Representations of hom-Lie algebras
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Cyclic homology for Hom-associative algebras
• Representations and module-extensions of hom 3-Lie algebras

Cited by in corpus (14)

• The construction and deformation of BiHom-Novikov agebras
• BiHom-Lie colour algebras structures
• On split regular BiHom-Leibniz superalgebras
• Cohomology and linear deformation of BiHom-left-symmetric algebras
• On Antipodes Of Hom-Hopf algebras
• Structures of BiHom-Poisson algebras
• (Non-BiHom-Commutative) BiHom-Poisson algebras
• Product and complex structures on 3-Bihom-Lie algebras
• On BiHom-analogue of generalized Lie algebras
• (Bi)Hom-Leibniz algebras
• On split regular BiHom-Poisson superalgebras
• Classification of multiplicative simple BiHom-Lie algebras
• The construction of 3-Bihom-Lie algebras
• BiHom-Poisson color algebras