Dissertation Enhancement: Noncommutative Dynamical Systems

论文增强：非交换动力系统

• 批准号: 9802696
• 负责人: Marius Dadarlat
• 金额: $ 3.45万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-05-15 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9802696&HistoricalAwards=false
• 关键词: Dissertation; Enhancement; Noncommutative; Dynamical; Systems

9802696 Dadarlat This award supports a twelve month NSF Dissertation Enhancement Award for Dr. Marius Dadarlat at the University of Tokyo, Tokyo, Japan. Dr. Dadarlat's student, Mr. Nathaniel P. Brown, will work with Dr. Yasuyuki Kawahigashi, Professor in the Department of Mathematics, on a research project entitled, "Noncummutative Dynamical Systems." A dynamical system is a mathematical model through which one attempts to understand the behavior of physical phenomena. The study of classical, or commutative, dynamical systems is closely related to many aspects of modern physics including both chaos and quantum theories. The proposed research will attempt to apply classical dynamical systems theory to the noncommutative setting and will investigate a series of geometric and algebraic questions concerning crossed product C*-algebras. The first component of the research will examine when certain classes of crossed product C*-algebras are embedded into AF algebras, allowing deduction concerning the specific geometric and algebraic properties of the crossed product C*-algebra. The second component of the research will build on some of the known classification results for crossed product C*-algebras; specifically, it will attempt to determine when certain crossed products are essentially the same. Finally, the research will attempt to develop an innovative notion of topological entropy for these noncommutative systems. Entropy has played an important role in the study of commutative systems, but entropy in the noncommutative setting is relatively new and not yet well understood. The research is designed to study this facet of mathematics with the goal of achieving concrete calculations for future examination. ***

9802696 Dadarlat该奖项为日本东京大学的Marius Dadarlat博士颁发了十二个月的NSF论文增强奖。 达达拉特（Dadarlat）博士的学生纳撒尼尔·P·布朗（Nathaniel P. 动态系统是一个数学模型，通过它试图理解物理现象的行为。 对经典或交换性动力学系统的研究与现代物理学的许多方面密切相关，包括混乱和量子理论。 拟议的研究将尝试将经典的动力系统理论应用于非共同设置，并将研究有关交叉产物C* - 代数的一系列几何和代数问题。 该研究的第一个组成部分将检查何时将某些类的交叉产物C* - 代数嵌入AF代数中，从而允许对交叉产物C*-Algebra的特定几何和代数特性进行扣除。 该研究的第二个组成部分将建立在交叉产物C* - 代数的一些已知分类结果的基础上。具体而言，它将尝试确定某些交叉产品何时基本相同。 最后，该研究将尝试为这些非交通性系统开发拓扑熵的创新概念。 熵在交换系统的研究中发挥了重要作用，但是在非交通环境中的熵相对较新，尚未得到充分理解。 该研究旨在研究这一数学方面，目的是实现具体计算以供将来检查。 ***