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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2015
• Main Authors: Graziani, G., Makhlouf, A., Menini, C., Panaite, F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147155
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras / G. Graziani, A. Makhlouf, C. Menini, F. Panaite // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 32 назв. — англ.

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 algebra...