二叉树、余积与可积系统
Binary trees, coproducts, and integrable systems
摘要：
我们提供了一个统一的框架来处理特殊的可积系统，我们建议称之为“广义平均场系统”。从而推广了以前关于可积经典和量子系统的结果。在巴列斯特罗斯和拉格尼斯科之后，这个框架由一个带括号的单位代数、一个卡西米尔元和一个可以提升到更高张量积的余积组成。迭代张量积的耦合方案被编码在二叉树中。该理论的例子是自旋八面体。
英文摘要：
We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.
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。
