Cohomology and linear deformation of BiHom-left-symmetric algebras

Abstract

The aim of this work is to introduce representations of BiHom-left-symmetric algebras. and develop its cohomology theory. As applications, we study linear deformations of BiHom-left-symmetric algebras, which are characterized by its second cohomology group with the coefficients in the adjoint representation. The notion of a Nijenhuis operator on a BiHom-left-symmetric algebra is introduced. We will prove that it can generate trivial linear deformations of a BiHom-left-symmetric algebra.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1902.07360 by other authors

References in corpus (7)

• Representations of hom-Lie algebras
• Nijenhuis operators on $n$-Lie algebras
• Representations of Bihom-Lie algebras
• BiHom-pre-Lie algebras, BiHom-Leibniz algebras and Rota-Baxter operators on BiHom-Lie algebras
• BiHom-Lie superalgebra structures
• BiHom-pre-alternative algebras and BiHom-alternative quadri-algebras
• Representations and cohomologies of Hom-pre-Lie algebras

Cited by in corpus (1)

• Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras