BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras

Abstract

A BiHom-associative algebra is a (nonassociative) algebra $A$ endowed with two commuting multiplicative linear maps $\alpha ,\beta :A\to A$ such that $\alpha (a)(bc)=(ab)\beta (c)$, for all $a,b,c\in A$. This concept arose in the study of algebras in so-called group Hom-categories. In this paper, we introduce as well BiHom-Lie algebras (also by using the categorical approach) and BiHom-bialgebras. We discuss these new structures by presenting some basic properties and constructions (representations, twisted tensor products, smash products etc).

References in corpus (4)

• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Module Hom-algebras
• Cyclic homology for Hom-associative algebras

Cited by in corpus (16)

• The construction and deformation of BiHom-Novikov agebras
• BiHom-pre-alternative algebras and BiHom-alternative quadri-algebras
• Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras
• Rota-Baxter operators on Turaev's Hopf group (co)algebras I: Basic definitions and related algebraic structures
• Tensor products and perturbations of BiHom-Novikov-Poisson algebras
• On Hom-Lie antialgebra
• On Antipodes Of Hom-Hopf algebras
• Nonhomogeneous associative Yang-Baxter equations
• Ado theorem for nilpotent Hom-Lie algebras
• Central invariants and enveloping algebras of braided Hom-Lie algebras
• Classification of multiplicative simple BiHom-Lie algebras
• Constructions and generalised derivations of multiplicative n-BiHom-Lie color algebras
• Product and complex structures on 3-Bihom-Lie algebras
• Hom-pre-Malcev and Hom-M-Dendriform algebras
• Representations, extensions and deformations of $n$-BiHom-Lie algebras
• The construction of 3-Bihom-Lie algebras