Classical Yang-Baxter equation and sheaves on degenerations of elliptic curves

椭圆曲线退化的经典Yang-Baxter方程和滑轮

• 批准号: 219669121
• 负责人: Professor Dr. Igor Burban
• 金额: --
• 依托单位: Fachgebiet Computeralgebra und Zahlentheorie
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/219669121?language=en
• 关键词: Classical; Yang; Baxter; equation; sheaves

We want to relate solutions of CYBE with simple torsion free coherent sheaveson curves of arithmetic genus one.1. Let Kp be the configuration of p generic concurrent projective lines in Pp-1 forp ≥ 3. We are going to studya) simple vector bundles on Kp,b) solutions of CYBE attached to the corresponding universal families,c) related algebraic structures: Frobenius functionals on seawead Lie algebras, representations of a bocses arising in the study of vector bundles on Kp etc.2. Establish a link between these results with problems of mathematical physics.

我们想把CYBE的解与算术亏格为1的曲线上的简单无挠相干剪切联系起来。设Kp是p-1中p条一般共点射影线的构形，p ≥ 3.我们将研究a）Kp上的简单向量丛，B）连接到相应泛族上的CYBE解，c）相关的代数结构：海味李代数上的Frobenius泛函，Kp上向量丛研究中产生的a bocses的表示等。建立这些结果与数学物理问题之间的联系。