Braces and the Yang-Baxter equation

大括号和 Yang-Baxter 方程

• 批准号: 2444997
• 金额: --
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2444997
• 关键词: Braces; Yang; Baxter; equation

We examine links between the theory of braces and set theoretical solutions of the Yang-Baxter equation, and fundamental concepts from the theory of quantum integrable systems. We also examine structure of braces. Recall that Braces, introduced in 2005 to construct set-theoretical solutions of the Yang-Baxter equation have links with many research areas, for example: Hopf-Galois extensions, Etale representations of Lie algebras, Pre-Lie algebras, Jacobson radical rings, among other topics. Among other topics we would like investigate symmetries of the transfer matrices and quantum integrable systems constructed from braces. Another possible topic is to investigate structure of braces by analogy with noncommutative ring theory. By Lazard's correspondence braces are connected to pre-Lie algebras (equivalent to right symmetric algebras) so obtained results can be generalised to the case of pre Lie algebras. On the other hand pre-Lie algebras correspond with Etale representations of affine Lie algebras which would give another application of results that we can obtain for braces.

我们将研究支撑理论与杨-巴克斯特方程的集合理论解之间的联系，以及量子可积系统理论的基本概念。我们还研究了大括号的结构。回想一下，在2005年引入的用于构造杨-巴克斯特方程的集合论解的括号与许多研究领域都有联系，例如：霍普夫-伽罗瓦扩张，李代数的Etale表示，前李代数，雅各布森根环等主题。在其他主题中，我们将研究转移矩阵的对称性和由大括号构造的量子可积系统。另一个可能的主题是通过与非交换环理论的类比来研究花括号的结构。由拉扎德的对应括号连接到前李代数（相当于右对称代数），所以得到的结果可以推广到前李代数的情况。另一方面，前李代数对应于Etale表示仿射李代数这将给另一个应用的结果，我们可以获得大括号。