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.

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

References in corpus (1)

• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras

Cited by in corpus (10)

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