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BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
Symmetry, integrability and geometry: methods and applications, Tome 11 (2015) Cet article a éte moissonné depuis la source Math-Net.Ru

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A BiHom-associative algebra is a (nonassociative) algebra $A$ endowed with two commuting multiplicative linear maps $\alpha , \beta\colon A\rightarrow A$ 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).
Keywords: BiHom-associative algebra; BiHom-Lie algebra; BiHom-bialgebra; representation; twisting; smash product. 
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     author = {Giacomo Graziani and Abdenacer Makhlouf and Claudia Menini and Florin Panaite},
     title = {BiHom-Associative {Algebras,} {BiHom-Lie} {Algebras} and {BiHom-Bialgebras}},
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}
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Giacomo Graziani; Abdenacer Makhlouf; Claudia Menini; Florin Panaite. BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras. Symmetry, integrability and geometry: methods and applications, Tome 11 (2015). http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a85/

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