Representations of Algebraic Groups in Differential and Difference Galois Theory

微分和差分伽罗瓦理论中代数群的表示

• 批准号: 123863936
• 负责人: Professorin Dr. Julia Hartmann
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/123863936?language=en
• 关键词: Representations; Algebraic; Groups; Differential; Difference

To a differential or difference equation one associates an algebraic group which describes the symmetries and encodes a lot of information about the solutions of the equation. By Tannakian theory, this group is determined by the structure of its representations on objects of the tensor category generated by the solution space. The aim of this project is to apply methods from the structure and representation theory of algebraic groups to study differential (or difference) equations. The first application is the computation of the symmetry group (Galois group) of a given equation. A second goal is the construction of objects with interesting symmetry groups.

对于微分方程或差分方程，人们会联想到一个代数群，它描述了对称性，并编码了关于方程解的大量信息。根据Tannakian理论，这个群由它在解空间生成的张量范畴的对象上的表示的结构决定。这个项目的目的是应用代数群的结构和表示理论的方法来研究微分（或差分）方程。第一个应用是计算给定方程的对称群（伽罗瓦群）。第二个目标是构造具有有趣对称群的物体。