BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
Graziani, Giacomo ; Makhlouf, Abdenacer ; Menini, Claudia ; Panaite, Florin
HAL, hal-01990618 / Harvested from HAL
Text on HAL
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).
Publié le : 2015-10-25
Classification:  [MATH]Mathematics [math] 
@article{hal-01990618,
     author = {Graziani, Giacomo and Makhlouf, Abdenacer and Menini, Claudia and Panaite, Florin},
     title = {BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras},
     journal = {HAL},
     volume = {2015},
     number = {0},
     year = {2015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01990618}
}

Graziani, Giacomo; Makhlouf, Abdenacer; Menini, Claudia; Panaite, Florin. BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras. HAL, Tome 2015 (2015) no. 0, . http://gdmltest.u-ga.fr/item/hal-01990618/