Anti-pre-Poisson bialgebras and relative Rota-Baxter operators
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908556379291648 |
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| author | Sun, Qinxiu Wu, Min |
| author_facet | Sun, Qinxiu Wu, Min |
| contents | In this paper, we first introduce the notion of an anti-pre-Poisson bialgebra, which is shown to be equivalent to both quadratic anti-pre-Poisson algebras and matched pairs of Poisson algebras. The study of coboundary anti-pre-Poisson bialgebras leads to the anti-pre-Poisson Yang-Baxter equation (APP-YBE). Skew-symmetric solutions of this equation give rise to coboundary anti-pre-Poisson bialgebras. Furthermore, we investigate how solutions without skew-symmetry can also induce such bialgebras, prompting the introduction of quasi-triangular and factorizable anti-pre-Poisson bialgebras. In particular, solutions of the APP-YBE whose symmetric parts are invariant induce a quasi-triangular anti-pre-Poisson bialgebra. Such solutions are also interpreted as relative Rota-Baxter operators with weights. Finally, we establish a one-to-one correspondence between quadratic Rota-Baxter anti-pre-Poisson algebras and factorizable anti-pre-Poisson bialgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13963 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anti-pre-Poisson bialgebras and relative Rota-Baxter operators Sun, Qinxiu Wu, Min Rings and Algebras In this paper, we first introduce the notion of an anti-pre-Poisson bialgebra, which is shown to be equivalent to both quadratic anti-pre-Poisson algebras and matched pairs of Poisson algebras. The study of coboundary anti-pre-Poisson bialgebras leads to the anti-pre-Poisson Yang-Baxter equation (APP-YBE). Skew-symmetric solutions of this equation give rise to coboundary anti-pre-Poisson bialgebras. Furthermore, we investigate how solutions without skew-symmetry can also induce such bialgebras, prompting the introduction of quasi-triangular and factorizable anti-pre-Poisson bialgebras. In particular, solutions of the APP-YBE whose symmetric parts are invariant induce a quasi-triangular anti-pre-Poisson bialgebra. Such solutions are also interpreted as relative Rota-Baxter operators with weights. Finally, we establish a one-to-one correspondence between quadratic Rota-Baxter anti-pre-Poisson algebras and factorizable anti-pre-Poisson bialgebras. |
| title | Anti-pre-Poisson bialgebras and relative Rota-Baxter operators |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2509.13963 |