循环余积
Loop coproducts
摘要：
本文证明了：如果$A$是一个Poisson代数，它具有一组满足适当条件的映射$Δ^{(i)}_\la:A \to A^{\otimes N}$，则$A$的Casimir函数在这些映射$Δ^{(i)}_\la$下的象（我们称之为“圈余积”）是对合的.理性，三角和椭圆Gaudin模型可以恢复为特殊情况下，这一结果，我们表明，同样发生的可积（或部分可积）模型，可以通过所谓的余积方法。另一方面，这种循环余积方法可能更普遍，并且可以将Gaudin代数从李泊松推广到泊松代数，并且希望定义新的可积模型。
英文摘要：
In this paper we show that if $A$ is a Poisson algebra equipped with a set of maps $Δ^{(i)}_\la:A \to A^{\otimes N}$ satisfying suitable conditions, then the images of the Casimir functions of $A$ under the maps $Δ^{(i)}_\la$ (that we call "loop coproducts") are in involution. Rational, trigonometric and elliptic Gaudin models can be recovered as particular cases of this result, and we show that the same happens for the integrable (or partially integrable) models that can be obtained through the so called coproduct method. On the other hand, this loop coproduct approach is potentially much more general, and could allow the generalization of the Gaudin algebras from the Lie-Poisson to the Poisson algebras context and, hopefully, the definition of new integrable models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
