课题基金 / 基金详情

Mathematical Sciences: Operator Algebras and Noncommutative Topology

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
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
1988
资助国家:
美国
项目状态:
已结题
起止时间:
1988-07-01 至 1990-12-31

项目摘要

项目成果

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相关文献

中文摘要
翻译
该项目是算子代数理论的数学研究。 该主题与拓扑关系的出发点是这样的情况:可交换的 C* 代数正是作为局部紧拓扑空间上的连续复值函数的代数而出现的代数。 (后一个代数包含足够的信息来完全恢复底层空间。)一般程序是将思想和构造从拓扑的交换设置扩展到算子代数的非交换领域。 需要研究的具体主题是:C*-代数范畴上同调和上同调理论的存在性和性质; K理论中的环结构;奇异空间上的运算符域;和不稳定的 K 理论,特别是对于简单的 C* 代数。
英文摘要
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.
期刊论文(0)
专著(0)
科研奖励(0)
会议论文
West Coast Operator Algebra Seminar; October 2-4, 2003; Alberta, Canada
Operator Algebras and Noncommutative Topology
U.S.-Japan Joint Seminar: Operator Algebras and Applications
Mathematical Sciences: Operator Algebras and Noncommutative Topology
国内基金
海外基金
Handbook of the Mathematics of the Arts and Sciences的中文翻译
  • 批准号:
    12226504
  • 项目类别:
    数学天元基金项目
  • 资助金额:
    20.0万元
  • 批准年份:
    2022
  • 负责人:
    黄朝凌
  • 依托单位:
SCIENCE CHINA: Earth Sciences
Journal of Environmental Sciences
SCIENCE CHINA Information Sciences