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

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Mathematics Pure mathematics Associative property Non-associative algebra Algebra over a field Universal enveloping algebra

Giacomo Graziani , Abdenacer Makhlouf , Claudia Menini , Florin Panaite ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.3842/sigma.2015.086 · OA: W2137253167

A BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α,β:A→A such that α(a)(bc)=(ab)β(c), for all a,b,c∈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).