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arXiv · 2509.13963

Anti-pre-Poisson bialgebras and relative Rota-Baxter operators

Qinxiu Sun·Min Wu
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Abstract

In this paper, we first introduce the notion of an anti-pre-Poisson bialgebra, which is shown to be equivalent to both quadratic anti-pre-Poisson algebras and matched pairs of Poisson algebras. The study of coboundary anti-pre-Poisson bialgebras leads to the anti-pre-Poisson Yang-Baxter equation (APP-YBE). Skew-symmetric solutions of this equation give rise to coboundary anti-pre-Poisson bialgebras. Furthermore, we investigate how solutions without skew-symmetry can also induce such bialgebras, prompting the introduction of quasi-triangular and factorizable anti-pre-Poisson bialgebras. In particular, solutions of the APP-YBE whose symmetric parts are invariant induce a quasi-triangular anti-pre-Poisson bialgebra. Such solutions are also interpreted as relative Rota-Baxter operators with weights. Finally, we establish a one-to-one correspondence between quadratic Rota-Baxter anti-pre-Poisson algebras and factorizable anti-pre-Poisson bialgebras.

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Qinxiu Sun, Min Wu. 2025-09-24. Anti-pre-Poisson bialgebras and relative Rota-Baxter operators. https://arxiv.org/abs/2509.13963

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