Mathematical Sciences: Quantized Analysis

数学科学：量化分析

• 批准号: 9206984
• 负责人: Masamichi Takesaki
• 金额: $ 38.01万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9206984&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Quantized; Analysis

Effros, Popa, and Takesaki will continue their investigations into operator algebra theory and its applications which can be phrased as "Quantized Analysis." Quantized Analysis is a key to understanding quantum phenomenon in mathematics and physics. Effros will continue his study of operator space analysis which is essential for building an analytic theory of quantum groups. Popa will continue his work on subfactor analysis based on his successful classification of amenable subfactors. Takesaki will continue his project on the cocycle conjugacy analysis of group actions on von Neumann algebras. 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.

埃弗罗斯、波帕和竹崎将继续调查 算子代数理论及其应用， 被称为“量化分析”。“量化分析是 理解数学和物理中的量子现象。 Effros将继续他的研究算子空间分析， 对建立量子群的分析理论至关重要。 波帕 将继续他的工作，在子因素分析的基础上， 成功地对顺从的子因子进行分类。 竹崎将 继续他的关于群的上循环共轭分析的项目 von Neumann algebra代数 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。