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博士提供为期12个月的NSF论文增强奖。Dadarlat博士的学生Nathaniel P. Brown先生将与数学系教授Yasuyuki Kawahigashi博士一起进行一个名为“非交换动力系统”的研究项目。动力系统是一种数学模型，人们试图通过它来理解物理现象的行为。经典或交换动力系统的研究与现代物理学的许多方面密切相关，包括混沌和量子理论。本研究将尝试将经典动力系统理论应用于非交换环境，并将研究一系列关于交叉积C*-代数的几何和代数问题。研究的第一个组成部分将检查何时将某些类型的交叉积C*-代数嵌入到AF代数中，从而允许推导有关交叉积C*-代数的特定几何和代数性质。研究的第二个组成部分将建立在交叉积C*-代数的一些已知分类结果上；具体来说，它将试图确定某些交叉产物何时本质上是相同的。最后，本研究将尝试为这些非交换系统发展一种创新的拓扑熵概念。熵在交换系统的研究中起着重要的作用，但熵在非交换环境中相对较新，尚未得到很好的理解。这项研究旨在研究数学的这一方面，目的是为将来的考试实现具体的计算。＊＊＊