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.

Effros，Popa和Takeaki将继续对操作员代数理论及其应用进行调查，以称为“量化分析”。 量化分析是了解数学和物理学中量子现象的关键。 EFFROS将继续他对操作员空间分析的研究，这对于建立量子组的分析理论至关重要。 Popa将基于他成功地分类的亚属​​子因子的分类继续他的子因素分析工作。 Takeaki将继续对冯·诺伊曼代数的团体行动进行共生共轭分析。 该项目数学的一般领域在希尔伯特太空运营商代数理论中具有其基础。 可以将操作员视为复数的有限或无限矩阵。 特殊类型的操作员通常将其放在代数中，自然称为操作员代数。 这些抽象对象具有令人惊讶的应用。 例如，它们在结理论中起着关键作用，而这反过来又被用来研究DNA的结构，并且在非交通性几何形状中至关重要，这在物理学中变得越来越重要。