Noncommutative pre-Poisson bialgebras and relative Rota-Baxter operators
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914349436633088 |
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| author | Li, Hongliang Sun, Qinxiu |
| author_facet | Li, Hongliang Sun, Qinxiu |
| contents | In this paper, we develop the bialgebra theory for coherent noncommutative pre-Poisson algebras and establish equivalences among matched pairs, Manin triples, the phase space of noncommutative Poisson algebras and noncommutative pre-Poisson bialgebras. The investigation of coboundary noncommutative pre-Poisson bialgebras naturally leads to the noncommutative pre-Poisson Yang-Baxter equation (NPP-YBE). We prove that a symmetric solution of the NPP-YBE gives rise to a (coboundary) noncommutative pre-Poisson bialgebra. Moreover, we demonstrate how solutions without the symmetry condition can also generate such bialgebras. This motivates the introduction of quasi-triangular and factorizable noncommutative pre-Poisson bialgebras.In particular, we show that a solution of the NPP-YBE with an invariant skew-symmetric part yields a quasi-triangular noncommutative pre-Poisson bialgebra.Such solutions are further interpreted as relative Rota-Baxter operators with weights. Finally, we establish a one-to-one correspondence between quadratic Rota-Baxter noncommutative pre-Poisson algebras and factorizable noncommutative pre-Poisson bialgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12908 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Noncommutative pre-Poisson bialgebras and relative Rota-Baxter operators Li, Hongliang Sun, Qinxiu Rings and Algebras Quantum Algebra 17A30, 17B63, 17B38, 16T10, 17B62 In this paper, we develop the bialgebra theory for coherent noncommutative pre-Poisson algebras and establish equivalences among matched pairs, Manin triples, the phase space of noncommutative Poisson algebras and noncommutative pre-Poisson bialgebras. The investigation of coboundary noncommutative pre-Poisson bialgebras naturally leads to the noncommutative pre-Poisson Yang-Baxter equation (NPP-YBE). We prove that a symmetric solution of the NPP-YBE gives rise to a (coboundary) noncommutative pre-Poisson bialgebra. Moreover, we demonstrate how solutions without the symmetry condition can also generate such bialgebras. This motivates the introduction of quasi-triangular and factorizable noncommutative pre-Poisson bialgebras.In particular, we show that a solution of the NPP-YBE with an invariant skew-symmetric part yields a quasi-triangular noncommutative pre-Poisson bialgebra.Such solutions are further interpreted as relative Rota-Baxter operators with weights. Finally, we establish a one-to-one correspondence between quadratic Rota-Baxter noncommutative pre-Poisson algebras and factorizable noncommutative pre-Poisson bialgebras. |
| title | Noncommutative pre-Poisson bialgebras and relative Rota-Baxter operators |
| topic | Rings and Algebras Quantum Algebra 17A30, 17B63, 17B38, 16T10, 17B62 |
| url | https://arxiv.org/abs/2602.12908 |