On Poisson conformal bialgebras

Yanyong Hong, Chengming Bai
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Abstract

We develop a conformal analog of the theory of Poisson bialgebras as well as a bialgebra theory of Poisson conformal algebras. We introduce the notion of Poisson conformal bialgebras, which are characterized by Manin triples of Poisson conformal algebras. A class of special Poisson conformal bialgebras called coboundary Poisson conformal bialgebras are constructed from skew-symmetric solutions of the Poisson conformal Yang-Baxter equation, whose operator forms are studied. Then we show that the semi-classical limits of conformal formal deformations of commutative and cocommutative antisymmetric infinitesimal conformal bialgebras are Poisson conformal bialgebras. Finally, we extend the correspondence between Poisson conformal algebras and Poisson-Gel'fand-Dorfman algebras to the context of bialgebras, that is, we introduce the notion of Poisson-Gel'fand-Dorfman bialgebras and show that Poisson-Gel'fand-Dorfman bialgebras correspond to a class of Poisson conformal bialgebras. Moreover, a construction of Poisson conformal bialgebras from pre-Poisson-Gel'fand-Dorfman algebras is given.
关于泊松保角双桥
我们发展了泊松双桥理论的保角类似理论以及泊松保角代数理论。我们引入了泊松保角双桥的概念,它的特征是泊松保角代数的马宁三元组。我们根据泊松保形阳-巴克斯特方程的斜对称解构建了一类特殊的泊松保形双玻,称为共边界泊松保形双玻,并对其算子形式进行了研究。然后,我们证明了交换和共交换反对称无限共形双桥的共形形式变形的半经典极限是泊松共形双桥。最后,我们把泊松共形双桥与泊松-Gel'fand-Dorfman 双桥之间的对应关系扩展到双桥的范畴,即引入泊松-Gel'fand-Dorfman 双桥的概念,并证明泊松-Gel'fand-Dorfman 双桥对应于一类泊松共形双桥。此外,还给出了由前泊松-Gel'fand-Dorfman双桥构建泊松保角双桥的方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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