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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2512.11540 |
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| _version_ | 1866909958439698432 |
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| author | Guo, Yanhong Hou, Bo |
| author_facet | Guo, Yanhong Hou, Bo |
| contents | The purpose of this paper is to construct infinite-dimensional Poisson bialgebras by the affinization of pre-Poisson algebras. There is a natural Poisson algebra structure on the tensor product of a pre-Poisson algebra and a perm algebra, and the Poisson algebra structure on the tensor product of a pre-Poisson algebra and a special perm algebra characterizes the pre-Poisson algebra. We extend such correspondences to the context of bialgebras, that is, there is a Poisson bialgebra structure on the tensor product of a pre-Poisson bialgebra and a quadratic $\bz$-graded perm algebra.In this process, we provide the affinization of Zinbiel bialgebras, and give a correspondence between symmetric solutions of the Yang-Baxter equation in pre-Poisson algebras and certain skew-symmetric solutions of the Yang-Baxter equation in the induced infinite-dimensional Poisson algebras. The similar correspondences for the related triangular bialgebra structures and $\mathcal{O}$-operators are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11540 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Affinization of Zinbiel bialgebras and pre-Poisson bialgebras, infinite-dimensional Poisson bialgebras Guo, Yanhong Hou, Bo Rings and Algebras Quantum Algebra The purpose of this paper is to construct infinite-dimensional Poisson bialgebras by the affinization of pre-Poisson algebras. There is a natural Poisson algebra structure on the tensor product of a pre-Poisson algebra and a perm algebra, and the Poisson algebra structure on the tensor product of a pre-Poisson algebra and a special perm algebra characterizes the pre-Poisson algebra. We extend such correspondences to the context of bialgebras, that is, there is a Poisson bialgebra structure on the tensor product of a pre-Poisson bialgebra and a quadratic $\bz$-graded perm algebra.In this process, we provide the affinization of Zinbiel bialgebras, and give a correspondence between symmetric solutions of the Yang-Baxter equation in pre-Poisson algebras and certain skew-symmetric solutions of the Yang-Baxter equation in the induced infinite-dimensional Poisson algebras. The similar correspondences for the related triangular bialgebra structures and $\mathcal{O}$-operators are given. |
| title | Affinization of Zinbiel bialgebras and pre-Poisson bialgebras, infinite-dimensional Poisson bialgebras |
| topic | Rings and Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2512.11540 |