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arXiv · 2504.18052

Manin triples, bialgebras and Yang-Baxter equation of $A_3$-associative algebras

Yaxi Jiang·Chuangchuang Kang·Jiafeng Lü
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Abstract

$A_3$-associative algebra is a generalization of associative algebra and is one of the four remarkable types of Lie-admissible algebras, along with associative algebra, left-symmetric algebra and right-symmetric algebra. This paper develops bialgebra theory for $A_3$-associative algebras. We introduce Manin triples and bialgebras for $A_3$-associative algebras, prove their equivalence using matched pairs of $A_3$-associative algebras, and define the $A_3$-associative Yang-Baxter equation and triangular $A_3$-associative bialgebras. Additionally, we introduce relative Rota-Baxter operators to provide skew-symmetric solutions of the $A_3$-associative Yang-Baxter equation.

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Yaxi Jiang, Chuangchuang Kang, Jiafeng Lü. 2025-04-25. Manin triples, bialgebras and Yang-Baxter equation of $A_3$-associative algebras. https://arxiv.org/abs/2504.18052

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