Mathematical Sciences: Structure of Operator Algebras

数学科学：算子代数的结构

• 批准号: 9111411
• 负责人: Vaughan Jones
• 金额: $ 12.09万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-15 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9111411&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Structure; Operator; Algebras

Professor Jones will study examples of subfactors (both from finite dimensional and infinite dimensional methods). His techniques will involve the use of loop group representations, knot theory, and statistical mechanics. Of special importance is an attempt to understand the correspondence between statistical mechanics and knot theory. This will be approached both by looking at large knots and a procedure called Baxterization. Jones' work has its basis in the theory of algebras of Hilbert space operators. These are families of linear functions on a certain type of infinite dimensional space. He is interested in how nests of these algebras fit inside one another. This seemingly technical subject turns out to have very important implications for a large variety of other areas of mathematics and physics including knot theory and the theory of three dimensional manifolds (topology) and statistical mechanics (physics).

琼斯教授将研究子因素的例子（无论是从 有限维和无限维方法）。 他 技术将涉及使用循环组表示、结 理论和统计力学。 特别重要的是， 试图理解统计数据之间的对应关系 力学和纽结理论 这将通过观察 在大的节和一个程序称为螺旋化。 琼斯的工作有其基础的理论代数的希尔伯特 太空操作员 这是一系列的线性函数， 某种无限维空间。 他感兴趣于 这些代数的嵌套是如何相互嵌套的 这个看似 技术主题对我们的研究 数学和物理学的许多其他领域，包括 纽结理论与三维流形理论 （拓扑学）和统计力学（物理学）。