论文标题
Adler-Oevel-Ragnisco类型操作员和泊松顶点代数
Adler-Oevel-Ragnisco type operators and Poisson vertex algebras
论文作者
论文摘要
基于end_f（g）中经典的R-Matrix r的泊松支架和相关集成系统的三元理论，其中g是一个有限的维度关联代数，该域被视为lie代数，是由Oevel-Ragnisco和li-Parementier [OR-Parementier [or89，lp89]开发的。 在本文中，我们通过介绍连续的泊松顶点代数的概念并构建了泊松兰伯达括号的三元组来开发该理论的“仿射”类似物。我们介绍了相应的Adler类型身份，并将其应用于哈密顿PDE的层次结构的整合性。
The theory of triples of Poisson brackets and related integrable systems, based on a classical R-matrix R in End_F(g), where g is a finite dimensional associative algebra over a field F viewed as a Lie algebra, was developed by Oevel-Ragnisco and Li-Parmentier [OR89,LP89]. In the present paper we develop an "affine" analogue of this theory by introducing the notion of a continuous Poisson vertex algebra and constructing triples of Poisson lambda-brackets. We introduce the corresponding Adler type identities and apply them to integrability of hierarchies of Hamiltonian PDEs.
