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arXiv · 2005.05064

Anti-flexible bialgebras

Mafoya Landry Dassoundo·Chengming Bai·Mahouton Norbert Hounkonnou
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Abstract

We establish a bialgebra theory for anti-flexible algebras in this paper. We introduce the notion of an anti-flexible bialgebra which is equivalent to a Manin triple of anti-flexible algebras. The study of a special case of anti-flexible bialgebras leads to the introduction of anti-flexible Yang-Baxter equation in an anti-flexible algebra which is an analogue of the classical Yang-Baxter equation in a Lie algebra or the associative Yang-Baxter equation in an associative algebra. It is a unexpected consequence that both the anti-flexible Yang-Baxter equation and the associative Yang-Baxter equation have the same form. A skew-symmetric solution of anti-flexible Yang-Baxter equation gives an anti-flexible bialgebra. Finally the notions of an $\mathcal O$-operator of an anti-flexible algebra and a pre-anti-flexible algebra are introduced to construct skew-symmetric solutions of anti-flexible Yang-Baxter equation.

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Mafoya Landry Dassoundo, Chengming Bai, Mahouton Norbert Hounkonnou. 2020-05-05. Anti-flexible bialgebras. https://doi.org/10.1142/s0219498822502127

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