Mathematical Sciences: Bialgebra Structures in the Theory ofRepresentations of Quantum Groups and the Quantum Yang-Baxter Equations

数学科学：量子群表示理论中的双代数结构和量子杨-巴克斯特方程

• 批准号: 9106222
• 负责人: David Radford
• 金额: $ 5.09万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9106222&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Bialgebra; Structures; Theory

This project is concerned with the construction of the quantum analogs of enveloping algebras, their representation theory, and solutions to the quantum Yang-Baxter equation on representation spaces. The principal investigator will use a module theoretic approach to the quantum Yang-Baxter equation. Particular emphasis will be given to classifying solutions in the 2-dimensional case. The class of finite dimensional quasitriangular Hopf algebras will also be studied with attention given to categorical constructions. Quantum groups are a new area of research for both mathematicians and physicists. On the mathematical side, it combines three of the oldest areas of "pure" mathematics, algebra, analysis and geometry, yet it is of great interest to physicists working in conformal quantum field theory.

本课题主要研究包络代数的量子类比的构造及其表示理论，以及表示空间上量子Yang-Baxter方程的解。主要研究人员将使用模理论方法来求解量子杨-巴克斯特方程。将特别强调对二维情况下的解决方案进行分类。有限维拟三角Hopf代数的类也将被研究，并注意范畴结构。量子群对数学家和物理学家来说都是一个新的研究领域。在数学方面，它结合了代数、分析和几何这三个最古老的纯数学领域，但它引起了从事共形量子场论工作的物理学家的极大兴趣。