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).

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

MENINI, Claudia;
2015

Abstract

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).
2015
Graziani, Giacomo; Makhlouf, Abdenacer; Menini, Claudia; Panaite, Florin
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2335407
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