Mathematical Sciences: Quantum Kac-Moody Groups and RelatedQuestions

数学科学：量子 Kac-Moody 群及相关问题

• 批准号: 9623327
• 负责人: Yan Soibelman
• 金额: $ 5.16万
• 依托单位: Kansas State University
• 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: 1996-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623327&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Quantum; Kac; Moody

9623327 Soibelman This grant supports the research of Professor Y. Soibelman to work on various problems in the theory of Kac-Moody groups. In particular he will study problems arising from the tensor structures in the theory of quantum affine algebras and compound versions of Lie bialgebras. He then will apply these results to quantum tau functions and quantum Weyl functions. Finally, he wishes to study chiral problems in the theory of quantum groups. 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.

9623327 Soibelman这笔赠款支持Y.Soibelman教授研究Kac-Moody群理论中的各种问题。特别是，他将研究量子仿射代数和李双代数的复合形式理论中的张量结构引起的问题。然后，他将把这些结果应用于量子tau函数和量子Weyl函数。最后，他希望研究量子群理论中的手征问题。这项研究始于代数领域，但超越了代数领域，触及了数论和理论物理。之所以有这些联系，是因为代数可以被认为是对抽象对称性的研究。因此，代数在物理和化学领域有直接的应用。特别是，现代物理学中的规范场理论广泛地使用了这一领域的代数，这个项目将详细研究其中的一些联系。此外，还与编码理论和跨通信线路的数据传输有关。