Mathematical Sciences: Operator Algebras and Noncommutative Topology

数学科学：算子代数和非交换拓扑

• 批准号: 8805342
• 负责人: Bruce Blackadar
• 金额: $ 5.24万
• 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: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8805342&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Operator; Algebras; Noncommutative

This project is mathematical research in the theory of operator algebras. The starting point for the relationship of this subject to topology is the circumstance that the commutative C*-algebras are precisely those that arise as the algebra of continuous complex-valued functions on a locally compact topological space. (The latter algebra contains enough information to recover completely the underlying space.) The general program is to extend ideas and constructions from the commutative setting of topology to the noncommutative realm of operator algebras. Specific topics to be investigated are: existence and properties of homology and cohomology theories on the category of C*-algebras; ring structure in K-theory; operator fields over singular spaces; and nonstable K-theory, especially for simple C*-algebras.

该项目是运营商代数理论中的数学研究。 该主题与拓扑之间关系的起点是，交换性c*代数恰好是在当地紧凑的拓扑空间上作为连续复杂值函数的代数出现的。 （后一个代数包含足够的信息来完全恢复基础空间。）一般计划是将思想和构造从拓扑的交换设置扩展到操作员代数的非交通域。 要研究的具体主题是：同源性和共同体学理论在C*-Algebras类别上的存在和特性； K理论中的环结构；奇异空间上的操作员字段；和不稳定的K理论，尤其是对于简单的C*-ergebras。