Mathematical Sciences: Trace Extensions and Commutator Spaces with Applications to the Homology, Determinants and K-Theory of Operator Ideals

数学科学：迹扩展和交换子空间及其在算子理想的同调、行列式和 K 理论中的应用

• 批准号: 9503062
• 负责人: Gary Weiss
• 金额: --
• 依托单位: University of Cincinnati Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9503062&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Trace; Extensions; Commutator

9503062 Weiss A principal goal of this project is to determine the Hochschild and cyclic cohomology groups for the full algebra of bounded Hilbert space operators relative to an arbitrary 2-sided ideal. These computations have been recently linked to characterizing commutator ideals. Trace extensions and the structure of commutators and commutator spaces will be investigated and exploited to yield information on the homology, determinants and K-theory of operator ideals. This project lies at the interface of two mathematical areas. On one side, the project concerns delicate explicit computations of commutators of operators. Operator theory evolved as an abstraction of the equations of mathematical physics. A commutator corresponds to the difference between ordered observations. In another direction, a collection of operators can often be considered as an algebraic structure called an operator algebra. Certain invariants of such algebras play an important role in several disciplines including mathematical physics and geometry. The purpose of this project is to realize these invariants by performing delicate commutator computations. ***

9503062 Weiss 该项目的主要目标是确定相对于任意 2 边理想的有界希尔伯特空间算子的完整代数的 Hochschild 和循环上同调群。这些计算最近已与表征换向器理想相关。将研究和利用迹线扩展以及换向器和换向器空间的结构，以产生有关算子理想的同源性、行列式和 K 理论的信息。 该项目位于两个数学领域的交界处。一方面，该项目涉及运算符换向器的精细显式计算。算子理论是作为数学物理方程的抽象而发展起来的。交换器对应于有序观察之间的差异。在另一个方向上，运算符的集合通常可以被视为称为运算符代数的代数结构。此类代数的某些不变量在包括数学物理和几何在内的多个学科中发挥着重要作用。该项目的目的是通过执行精细的换向器计算来实现这些不变量。 ***