C*-Algebras and Dynamical Systems

C*-代数和动力系统

• 批准号: 0355273
• 负责人: Huaxin Lin
• 金额: $ 10.5万
• 依托单位: University of Oregon Eugene
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2007-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0355273&HistoricalAwards=false
• 关键词: Algebras; Dynamical; Systems

AbstractLinThe main goal of this project is to classify nuclear simple C*-algebras by their K-theoretical data. The principal investigator introduced a notion of tracial topological rank for C*-algebras. It has been established that this new rank is quite useful in classification of nuclear simple C*-algebras. The investigator proposes to classify unital simple nuclear C*-algebras with tracial topological rank no more than one by their K-theoretical data. These C*-algebras include most known nuclear simple C*-algebras. The investigator also proposes to determine tracial topological ranks for many naturally occurred simple C*-algebras.The simplest examples of noncommutative C*-algebras are collections of matrices. In general, C*-algebras could be thought as collections of infinite matrices. In quantum mechanics physical quantities are represented by operators on a Hilbert space i.e. by infinite matrices. C*-algebras appeared as an outgrowth of quantum physics. But C*-algebras also provide the natural framework for generalizing geometry, topology and measure theory in a fundamental noncommutative way of wide applicability. Simple C*-algebras can be viewed as the key to understanding quantum variables. They are the fundamental building blocks of more general C*-algebras as well as the typical noncommutative C*-algebras. This research project is to study how to describe these C*-algebras via a few data which is topological in nature. Immediate applications can be established in the study of dynamical systems.

AbstractLin 该项目的主要目标是通过 K 理论数据对核简单 C* 代数进行分类。 主要研究者引入了 C* 代数的轨迹拓扑等级的概念。已经证实，这个新的等级对于核简单 C* 代数的分类非常有用。 研究人员建议根据 K 理论数据对拓扑秩不超过 1 的单位简单核 C* 代数进行分类。这些 C* 代数包括最知名的核简单 C* 代数。 研究人员还建议确定许多自然发生的简单 C* 代数的轨迹拓扑等级。非交换 C* 代数最简单的例子是矩阵的集合。一般来说，C* 代数可以被认为是无限矩阵的集合。 在量子力学中，物理量由希尔伯特空间上的算子表示，即由无限矩阵表示。 C*-代数作为量子物理学的产物出现。 但 C* 代数还提供了以具有广泛适用性的基本非交换方式推广几何、拓扑和测度论的自然框架。 简单的 C* 代数可以被视为理解量子变量的关键。它们是更一般的 C* 代数以及典型的非交换 C* 代数的基本构建块。 本研究项目旨在研究如何通过一些具有拓扑性质的数据来描述这些C*代数。 可以在动力系统的研究中立即应用。