Mathematical Sciences: Analytical and Combinatorial Aspects of Subfactors

数学科学：子因子的分析和组合方面

• 批准号: 9307234
• 负责人: Vaughan Jones
• 金额: $ 5.23万
• 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: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9307234&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytical; Combinatorial; Aspects

Bisch will construct and analysis irreducible subfactors of the hyperfinite II_1 factor using the combinatorial aspects of subfactors and commuting squares. He will also study connections between subfactors, quantum physics, and low dimensional topology. Finally, he will study subfactors of free group factors. The key technique here will be Voiculescu's free probability theory. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA, and they are of fundamental importance in noncommutative geometry, which is becoming increasingly important in physics.

Bisch将构造和分析 超有限II_1因子使用的组合方面 子因子和通勤广场。 他还将研究 子因子、量子物理和低维拓扑之间的联系。 最后，他将研究自由组因子的子因子。 关键 这里的技术是Voiculescu的自由概率论。 这个项目的一般数学领域有其基础 希尔伯特空间算子的代数理论。 运营商 可以被认为是复数的有限或无限矩阵 号码 特殊类型的运算符通常放在 代数，自然称为算子代数。 这些抽象 物体的应用范围之广令人惊讶。 比如说， 它们在纽结理论中起着关键作用，而纽结理论目前 被用来研究DNA的结构， 在非对易几何中的重要性， 在物理学中变得越来越重要。