Extending structures for pre-Poisson algebras and pre-Poisson bialgebras
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908329361539072 |
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| author | Zhu, Qianwen Liu, Guilai Sun, Qinxiu |
| author_facet | Zhu, Qianwen Liu, Guilai Sun, Qinxiu |
| contents | In this paper, we explore the extending structures problem by the unified product for pre-Poisson algebras. In particular, the crossed product and the factorization problem are investigated. Furthermore, a special case of extending structures is studied under the case of pre-Poisson algebras, which leads to the discussion of bicrossed products and matched pairs of pre-Poisson algebras. We develop a bialgebra theory for pre-Poisson algebras and establish the equivalence between matched pairs and pre-Poisson bialgebras. We study coboundary pre-Poisson bialgebras, which lead to the introduction of the pre-Poisson Yang-Baxter equation (PPYBE). A symmetric solution of the PPYBE naturally gives a coboundary pre-Poisson bialgebra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_15092 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending structures for pre-Poisson algebras and pre-Poisson bialgebras Zhu, Qianwen Liu, Guilai Sun, Qinxiu Rings and Algebras 17B62, 17B63, 17A30, 16T25 In this paper, we explore the extending structures problem by the unified product for pre-Poisson algebras. In particular, the crossed product and the factorization problem are investigated. Furthermore, a special case of extending structures is studied under the case of pre-Poisson algebras, which leads to the discussion of bicrossed products and matched pairs of pre-Poisson algebras. We develop a bialgebra theory for pre-Poisson algebras and establish the equivalence between matched pairs and pre-Poisson bialgebras. We study coboundary pre-Poisson bialgebras, which lead to the introduction of the pre-Poisson Yang-Baxter equation (PPYBE). A symmetric solution of the PPYBE naturally gives a coboundary pre-Poisson bialgebra. |
| title | Extending structures for pre-Poisson algebras and pre-Poisson bialgebras |
| topic | Rings and Algebras 17B62, 17B63, 17A30, 16T25 |
| url | https://arxiv.org/abs/2504.15092 |