Mathematical Sciences: Cohomology of Operator Algebras

数学科学：算子代数的上同调

• 批准号: 9007757
• 负责人: Frank Gilfeather
• 金额: $ 2.79万
• 依托单位: University of New Mexico
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9007757&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cohomology; Operator; Algebras

Professor Gilfeather will investigate cohomology in operator algebras by extending natural topological constructions to a non-commutative setting. The expectation is that his work will lead to a better understanding of the cohomology of non- selfadjoint operator algebras and will therefore have a substantial impact on our understanding of these algebras. This research originates in the study of operators on Hilbert space. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important categories of such objects.

Gilfeather教授将研究算子的上同调 将自然拓扑结构推广到代数 非交换设置。 人们期望他的工作将 从而更好地理解非线性系统的上同调， 自伴算子代数，因此有一个 对我们理解这些代数产生了巨大的影响。 本研究源于对运营商的研究， Hilbert空间 希尔伯特空间算子本质上是无限的 复数的矩阵 这些运营商有应用程序 在应用科学和纯数学的各个领域都是如此。 这种类型的研究是试图将某些重要的 这类物体的种类。