Manin triples, bialgebras and Yang-Baxter equation of $A_3$-associative algebras
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arXiv
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| Format: | Preprint |
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2025
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| author | Jiang, Yaxi Kang, Chuangchuang Lü, Jiafeng |
| author_facet | Jiang, Yaxi Kang, Chuangchuang Lü, Jiafeng |
| contents | $A_3$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18052 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Manin triples, bialgebras and Yang-Baxter equation of $A_3$-associative algebras Jiang, Yaxi Kang, Chuangchuang Lü, Jiafeng Rings and Algebras 16T10, 16T25, 16W10, 17A30, 17B62 $A_3$-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. |
| title | Manin triples, bialgebras and Yang-Baxter equation of $A_3$-associative algebras |
| topic | Rings and Algebras 16T10, 16T25, 16W10, 17A30, 17B62 |
| url | https://arxiv.org/abs/2504.18052 |