Quantum Algebras, coalgebras and Invariants of Knots, Links and 3-Manifolds

量子代数、余代数以及结、链和 3 流形的不变量

• 批准号: 9802178
• 负责人: David Radford
• 金额: $ 11.09万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-06-01 至 2002-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9802178&HistoricalAwards=false
• 关键词: Quantum; Algebras; coalgebras; Invariants; Knots

RADFORD, 98-02178 Abstract The proposer will continue his long term investigation into invariants of knots, 1-1 tangles and 3-manifolds which arise from various algebraic structures. The focus of this phase of his work is the study of quantum coalgebras and the invariants they determine. They account for the invariants which arise from finite dimensional quantum algebras. Coquasitriangular Hopf algebras are examples of quantum coalgebras. Hopf algebras and quantum groups are algebraic objects whose study is important in contemporary physics and also which have application to geometric and topological problems. Knot theory has seen applications in the studying molecular structure.

拉德福，98-02178 摘要 提出者将继续他的长期研究纽结，1-1缠结和3-流形，从各种代数结构产生的不变量。这一阶段的工作重点是研究量子余代数及其确定的不变量。它们解释了由有限维量子代数产生的不变量。余拟三角Hopf代数是量子余代数的例子。 Hopf代数和量子群是代数学的对象，它们的研究在当代物理学中具有重要意义，并且在几何学和拓扑学中也有应用 问题纽结理论在分子结构研究中得到了应用。