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 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).
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