Representations of Bihom-Lie algebras

2016/10/14 by Yongsheng Cheng, Cheng, Yongsheng, Huange Qi +1 · 4 citations
Mathematics · #17B10 #17B65 #17B68 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1610.04302

openalex publication_date 2016/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On Hom–Lie algebras

Cited by

• (Non-BiHom-Commutative) BiHom-Poisson algebras
• Product and complex structures on 3-Bihom-Lie algebras
• Structures of BiHom-Poisson algebras
• BiHom-Lie colour algebras structures

Related

• Representations, extensions and deformations of n-BiHom-Lie algebras
• BiHom-Lie colour algebras structures
• Constructions and representation theory of BiHom-post-Lie algebras
• Split extensions of BiHom-Lie algebras
• Cohomology and derivations of BiHom-Lie conformal algebras