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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2602.10669 |
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| _version_ | 1866918332253339648 |
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| author | Hou, Bo Li, Ru |
| author_facet | Hou, Bo Li, Ru |
| contents | In this paper, the notions of quasi-triangular and factorizable dual pre-Poisson bialgebras are introduced. A factorizable dual pre-Poisson bialgebra induces a factorization of the underlying dual pre-Poisson algebra, and the double of any dual pre-Poisson bialgebra is factorizable. We introduce the notion of quadratic Rota-Baxter dual pre-Poisson algebras and show that there is a one-to-one correspondence between factorizable dual pre-Poisson bialgebras and quadratic Rota-Baxter Poisson algebras of nonzero weights. Moreover, a method of constructing infinite-dimensional dual pre-Poisson bialgebras using finite-dimensional Poisson bialgebras is given. We prove that there is a completed dual pre-Poisson bialgebra structure the tensor product of a Poisson bialgebra and a quadratic $\bz$-graded perm algebra, and this completed dual pre-Poisson bialgebra structure is coboundary (resp. quasi-triangular, triangular) if the original Poisson bialgebra is coboundary (resp. quasi-triangular, triangular). The induced factorizable finite-dimensional dual pre-Poisson bialgebras are considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10669 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-triangular dual pre-Poisson bialgebras and its connection with Poisson bialgebras Hou, Bo Li, Ru Rings and Algebras Quantum Algebra In this paper, the notions of quasi-triangular and factorizable dual pre-Poisson bialgebras are introduced. A factorizable dual pre-Poisson bialgebra induces a factorization of the underlying dual pre-Poisson algebra, and the double of any dual pre-Poisson bialgebra is factorizable. We introduce the notion of quadratic Rota-Baxter dual pre-Poisson algebras and show that there is a one-to-one correspondence between factorizable dual pre-Poisson bialgebras and quadratic Rota-Baxter Poisson algebras of nonzero weights. Moreover, a method of constructing infinite-dimensional dual pre-Poisson bialgebras using finite-dimensional Poisson bialgebras is given. We prove that there is a completed dual pre-Poisson bialgebra structure the tensor product of a Poisson bialgebra and a quadratic $\bz$-graded perm algebra, and this completed dual pre-Poisson bialgebra structure is coboundary (resp. quasi-triangular, triangular) if the original Poisson bialgebra is coboundary (resp. quasi-triangular, triangular). The induced factorizable finite-dimensional dual pre-Poisson bialgebras are considered. |
| title | Quasi-triangular dual pre-Poisson bialgebras and its connection with Poisson bialgebras |
| topic | Rings and Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2602.10669 |