Giacomo Graziani, Abdenacer Makhlouf, Claudia Menini, Florin Panaite
2015.5.3Symmetry Integrability and Geometry-Methods and Applications
tlooto Summary
A BiHom-associative algebra is a nonassociative algebra with two commuting multiplicative linear maps.
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).
Citation format
GRAZIANI, Giacomo, et al. Bihom-associative algebras, bihom-lie algebras and bihom-bialgebras [preprint]. arXiv, 2015. arXiv:1505.00469.