Center-symmetric algebras and bialgebras: relevant properties and consequences
Abstract
Lie admissible algebra structures, called center-symmetric algebras, are defined. Main properties and algebraic consequences are derived and discussed. Bimodules are given and used to build a center-symmetric algebra on the direct sum of underlying vector space and a finite dimensional vector space. Then, the matched pair of center-symmetric algebras is established and related to the matched pair of sub-adjacent Lie algebras. Besides, Manin triple of center-symmetric algebras is defined and linked with their associated matched pairs. Further, center-symmetric bialgebras of center-symmetric algebras are investigated and discussed. Finally, a theorem yielding the equivalence between Manin triple of center-symmetric algebras, matched pairs of Lie algebras and center-symmetric bialgebras is provided.
Keywords
Cite
@article{arxiv.1507.07718,
title = {Center-symmetric algebras and bialgebras: relevant properties and consequences},
author = {Mahouton Norbert Hounkonnou and Mafoya Landry Dassoundo},
journal= {arXiv preprint arXiv:1507.07718},
year = {2015}
}