Mathematical Sciences: C*-Algebra Extensions and Homomorphisms

数学科学：C*-代数扩展和同态

• 批准号: 9301082
• 负责人: Huaxin Lin
• 金额: $ 3.98万
• 依托单位: SUNY at Buffalo
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1995-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301082&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebra; Extensions; Homomorphisms

Lin will work to obtain an extension of the Weyl-von Neumann theorem which will be used to give a complete classification of C*- algebra extensions of C(X), X a compact subset of the plane, by a sigma unital simple C*-algebra. He will also investigate whether every C*-algebra of real rank zero has weak (FN), as has been shown by Lin in many cases. A final problem to be studied is that of classifying certain equivalence classes of homomorphisms from one C*-algebra to another. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA, and they are of fundamental importance in non-commutative geometry, which is becoming increasingly important in physics.

Lin将致力于得到Weyl-von Neumann定理的一个推广，它将被用来给出C(X)的C*-代数扩张的完全分类，X是平面的一个紧子集，是一个sigma单位元的单C*-代数。他还将研究是否每个实秩零的C*-代数都有弱(Fn)，正如Lin在许多情况下所证明的那样。要研究的最后一个问题是将同态的某些等价类从一个C*-代数分类到另一个C*-代数。这个项目的一般数学领域以希尔伯特空间算子的代数理论为基础。运算符可以被认为是复数的有限或无限矩阵。特殊类型的运算符通常放在一个代数中，自然称为运算符代数。这些抽象对象具有令人惊讶的各种应用。例如，它们在纽结理论中扮演着关键的角色，而纽结理论目前正被用于研究DNA的结构，并且它们在非对易几何中具有基本的重要性，这在物理学中变得越来越重要。