Open Access
December 2020 q-generalized (anti -) flexible algebras and bialgebras
Mahouton Norbert Hounkonnou, Mafoya Landry Dassoundo
Author Affiliations +
SUT J. Math. 56(2): 71-92 (December 2020). DOI: 10.55937/sut/1610363822


In this work, we provide a q-generalization of flexible algebras and related bialgebraic structures, including center-symmetric (also called anti-flexible) algebras, and their bialgebras. Their basic properties are derived and discussed. Their connection with known algebraic structures, previously developed in the literature, is established. A q-Myung theorem is given. Main properties related to bimodules, matched pairs and dual bimodules as well as their algebraic consequences are investigated and analyzed. Besides, the equivalence between q-generalized flexible algebras, their Manin triple and bialgebras is established. Finally, various remarkable identities are established for the octonion algebra.

Funding Statement

This work is partially supported by TWAS Research Grant RGA No.17-542 RG /MATHS /AF/AC GFR3240300147. The ICMPAUNESCO Chair is in partnership with the Association pour la Promotion Scientifique de l’Afrique (APSA), France, and Daniel Iagolnitzer Foundation (DIF), France, supporting the development of mathematical physics in Africa.


The authors thank the referees for their useful comments which allow to improve the paper.


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Mahouton Norbert Hounkonnou. Mafoya Landry Dassoundo. "q-generalized (anti -) flexible algebras and bialgebras." SUT J. Math. 56 (2) 71 - 92, December 2020.


Received: 28 May 2018; Published: December 2020
First available in Project Euclid: 8 June 2022

Digital Object Identifier: 10.55937/sut/1610363822

Primary: 16D20 , 16T10 , 16-XX , 16Yxx , 17A30 , 17Axx , 17D25 , 17D99
Secondary: 16S80 , 16T25

Keywords: (anti-)flexible algebra , bialgebra , Lie-admissible algebra , Manin triple , matched pair

Rights: Copyright © 2020 Tokyo University of Science

Vol.56 • No. 2 • December 2020
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