Poisson Yang-Baxter equations and $\mathcal{O}$-operators of Poisson superalgebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916665212534784 |
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| author | Shan, Jiawen Zhang, Runxuan |
| author_facet | Shan, Jiawen Zhang, Runxuan |
| contents | We investigate connections between $\mathcal {O}$-operators of Poisson superalgebras and skew-symmetric solutions of the Poisson Yang-Baxter equation (PYBE). We prove that a skew-symmetric solution of the PYBE on a Poisson superalgebra can be interpreted as an $\mathcal {O}$-operator associated to the co-regular representation. We show that this connection can be enhanced with symplectic forms when considering non-degenerate skew-symmetric solutions. We also show that $\mathcal {O}$-operators associated to a general representation could give skew-symmetric solutions of the PYBE in certain semi-direct product of Poisson superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_02064 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Poisson Yang-Baxter equations and $\mathcal{O}$-operators of Poisson superalgebras Shan, Jiawen Zhang, Runxuan Rings and Algebras Mathematical Physics We investigate connections between $\mathcal {O}$-operators of Poisson superalgebras and skew-symmetric solutions of the Poisson Yang-Baxter equation (PYBE). We prove that a skew-symmetric solution of the PYBE on a Poisson superalgebra can be interpreted as an $\mathcal {O}$-operator associated to the co-regular representation. We show that this connection can be enhanced with symplectic forms when considering non-degenerate skew-symmetric solutions. We also show that $\mathcal {O}$-operators associated to a general representation could give skew-symmetric solutions of the PYBE in certain semi-direct product of Poisson superalgebras. |
| title | Poisson Yang-Baxter equations and $\mathcal{O}$-operators of Poisson superalgebras |
| topic | Rings and Algebras Mathematical Physics |
| url | https://arxiv.org/abs/2103.02064 |