Mathematical Sciences: Vertex Operator Algebras and their Relations with Posisson Lie Algebras

数学科学：顶点算子代数及其与泊西松李代数的关系

• 批准号: 9616630
• 负责人: Haisheng Li
• 金额: $ 6万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-09-01 至 1999-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9616630&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Vertex; Operator; Algebras

9616630 Li This grant supports the research of Professor H. Li to work on various problems in the theory of vertex operators. He wishes to show that certain holomorphic vertex operators of degree 24 exist, to work on the rationality of some W-algebras and to establish an equivalent functor from the category of vertex algebras and the category of Poisson Lie algebras. This is research that starts out in the field of algebra but moves beyond that to touch both number theory and theoretical physics. The reasons for these connections are that algebra can be though of as the study of symmetry in the abstract. As such algebra has direct applications to areas of physics and chemistry. In particular the modern theory of gauge fields in physics uses this area of algebra extensively and this project will study some of these connections at length. There are also connections to coding theory and the transmission of data across communication lines.

9616630李这笔赠款支持H. Li教授的研究，以解决顶点操作员理论中的各种问题。他希望表明，有24度的某些全体形态顶点操作员存在一些W-Algebras的合理性，并从顶点代数的类别和Poisson Like Like lie代数建立同等函数。 这是从代数领域开始的研究，但超越了触摸数字理论和理论物理学。 这些连接的原因是代数可以作为抽象的对称性研究。因此，这种代数直接应用于物理和化学领域。特别是，物理学量规场的现代理论广泛使用了代数的这一区域，该项目将详细研究其中一些连接。与编码理论以及跨通信线的数据传输也有连接。