Simple C*-Algebras

简单的 C* 代数

基本信息

批准号：
0097903
负责人：
Huaxin Lin
金额：
$ 9.86万
依托单位：
University of Oregon Eugene
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2001
资助国家：
美国
起止时间：
2001-06-01 至 2004-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0097903&HistoricalAwards=false
关键词：
Simple Algebras

项目摘要

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.

摘要该项目的主要目标是通过其k理论数据对核简单的C* - 代数进行分类。首席研究人员提出了C*代数的奇异拓扑等级的概念。已经确定，这个新等级在核简单C*代数的分类中非常有用。研究人员建议将Unital简单的核C*代数分类为奇学数据不超过一个。这些C* - 代数包括最著名的核简单C* - 代数。研究者还建议确定许多天然发生的简单C* - 代数的曲折拓扑等级。非交通性C* - 代数的最简单示例是矩阵的集合。通常，可以将C* - 代数视为无限矩阵的集合。在量子力学中，物理量由运营商在希尔伯特空间（即无限矩阵）上表示。 C* - 代数似乎是量子物理学的产物。但是C*-代数还提供了自然框架，以一种基本的非共同方式的广泛适用性方式概括几何形状，拓扑和测量理论。简单的C* - 代数可以看作是了解量子变量的关键。它们是更通用的C* - 代数以及典型的非交易性C* - 代数的基本构建块。该研究项目是研究如何通过本质上拓扑的一些数据来描述这些c* - 代数。可以在动态系统的研究中建立直接应用。