Mathematical Sciences: Yang-Baxter Operators, Quantum Field Theories and Invariants in Low-Dimensional Topology via HopfAlgebras and Representations of Monoidal Categories

数学科学：Yang-Baxter 算子、量子场论和低维拓扑中的不变量（通过 Hopf 代数和幺半群表示）

• 批准号: 9003741
• 负责人: David Yetter
• 金额: $ 2.97万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1991-10-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003741&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Yang; Baxter; Operators

Yetter will explore several aspects of the recently discovered interactions between low-dimensional topology, statistical mechanics, quantum field theory, Hopf algebra and monoidal category theory. In particular, he will use Hopf algebra and category theoretic techniques to construct and, if possible, classify 1) solutions to the quantum Yang-Baxter equation and 2) topological and conformal quantum field theories. Even partial results would shed light on the meaning and interrelations of the newly discovered polynomial invariants of classical knots and links.

Yetter将探讨最近的几个方面， 发现了低维拓扑之间的相互作用， 统计力学，量子场论，霍普夫代数和 monoidal范畴理论 特别是，他将使用霍普夫代数和范畴 理论技术来构建，如果可能的话，分类1） 量子Yang-Baxter方程的解和2）拓扑 和共形量子场论 即使是部分结果， 揭示了新的意义和相互关系， 发现了经典节点和链接的多项式不变量。