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arXiv · 2103.02064

Poisson Yang-Baxter equations and $\mathcal{O}$-operators of Poisson superalgebras

Jiawen Shan·Runxuan Zhang
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Abstract

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.

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Jiawen Shan, Runxuan Zhang. 2021-03-02. Poisson Yang-Baxter equations and $\mathcal{O}$-operators of Poisson superalgebras. https://arxiv.org/abs/2103.02064

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