Mathematical Sciences: K-Theory of C*-Algebras, Group Representations, and Coarse Geometry

数学科学：C* 代数的 K 理论、群表示和粗略几何

• 批准号: 9500977
• 负责人: Nigel Higson
• 金额: $ 10.1万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500977&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; Algebras; Group

9500977 Higson This project deals with the Baum-Connes conjecture. The emphasis of the project is not so much on proving new cases of the conjecture as on trying to understand more clearly the connections between the conjecture and the presumably related topics in geometry and representation theory. The long term goal is to use points of view suggested by the conjecture to give new insights into these subjects. Taking advantage of the extremely broad scope of the conjecture (which reaches from the Novikov conjecture to p-adic group representation theory) one might hope to forge new links between apparently dissimilar areas. The work proposed represents some very modest first steps in this direction. The general area of mathematics of this project has its basis in the theory of algebras of operators on Hilbert space. 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 seemingly 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. ***

9500977希格森 这个项目涉及Baum-Connes猜想。该项目的重点不是证明新的情况下的猜想，试图更清楚地了解之间的联系猜想和可能相关的主题在几何和表示论。长期的目标是使用的观点所建议的猜想，给新的见解，这些问题。利用这个猜想的极其广泛的范围（从诺维科夫猜想到p-adic群表示论），人们可能希望在明显不同的领域之间建立新的联系。拟议的工作是朝这个方向迈出的一些非常有限的第一步。 这个项目的一般数学领域有其基础的理论代数的运营商在希尔伯特空间。运算符可以被认为是复数的有限或无限矩阵。特殊类型的算子通常被放在一个代数中，自然称为算子代数。这些看似抽象的物体有着令人惊讶的多种应用。例如，它们在纽结理论中起着关键作用，而纽结理论目前正被用于研究DNA的结构。 ***