Operator Algebras and Noncommutative Topology

算子代数和非交换拓扑

• 批准号: 0070763
• 负责人: Bruce Blackadar
• 金额: $ 9万
• 依托单位: Board of Regents, NSHE, obo University of Nevada, Reno
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070763&HistoricalAwards=false
• 关键词: Operator; Algebras; Noncommutative; Topology

ABSTRACTBlackadarBlackadar will study a range of questions concerning the structure of variousclasses of operator algebras and their relation to noncommutative topology.Topics will include generalized inductive limits of finite-dimensionalC*-algebras and the structure of nuclear C*-algebras, semiprojectivity,nonstable K-theory and the Universal Coefficient Theorem, and bivariantcohomology theories on C*-algebras and their dense subalgebras.An idea which has revolutionized the study of operator algebras in recentyears, and which has led to some spectacular applications throughoutmathematics and mathematical physics, is to view operator algebras asgeneralizations of topological spaces, or more precisely the set ofcontinuous functions on a topological space; the principal new featureis that the multiplication of "functions" is no longer assumed to becommutative. It has long been recognized that operator algebras provide the "right" framework for the mathematical formulation of quantum mechanics, and it has been increasingly recognizedrecently that noncommutative "function spaces" (operator algebras)arise naturally in problems in subjects as diverse as knot theory(with applications to the structure of DNA and other molecules, as wellas mathematical physics), dynamical systems, and even mathematical logic.It has become apparent that it will be possible to give an explicitdescription of all operator algebras in large classes, including mostalgebras arising in applications, far beyond what was thought possibleonly a few years ago. This project concerns some of the centralremaining problems in the classification of one particularly importantclass, the nuclear C*-algebras. Understanding the mathematical structuresthat can occur will give great insight into the nature and behavior ofthe associated applied problems.

Abstractblackadarblackadar将研究一系列有关操作员代数的结构的问题及其与非交通性拓扑的关系。主题将包括有限的二量化和核C* - 核C* - 核心，非稳定性Khearory and thar and of comiant and thar and thar and thar and of有限的电位限制的通用电感限制。 C*-Algebras及其茂密的次级代理。一种彻底改变了对循环系统的操作员代数研究的想法，这导致了整个跨膜和数学物理学的某些观点应用，是为了查看操作员代数Asergebras Aseralizations of Generallizations of topological Space，或者更明确地在一系列拓扑函数上均可使用拓扑函数;不再假定“函数”乘法的主要新功能。 It has long been recognized that operator algebras provide the "right" framework for the mathematical formulation of quantum mechanics, and it has been increasingly recognizedrecently that noncommutative "function spaces" (operator algebras)arise naturally in problems in subjects as diverse as knot theory(with applications to the structure of DNA and other molecules, as wellas mathematical physics), dynamical systems, and even mathematical逻辑。显然，可以在大型类别中对所有操作员代数（包括在应用中产生的大多数级别的代数）进行明确描述，这远远超出了几年前可能的可能。 该项目涉及一个特别重要阶级核C* - 代数的分类中的一些中心问题。 了解可能发生数学结构的结构，将对相关应用问题的性质和行为有充分的了解。