Mathematical Sciences: Crossed Product Algebras, Non-Commutatuve Duality, and Applications to Group Representations

数学科学：叉积代数、非交换对偶性以及群表示的应用

• 批准号: 8801448
• 负责人: Elliot Gootman
• 金额: $ 3.99万
• 依托单位: University of Georgia Research Foundation Inc
• 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: 1988-06-15 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801448&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Crossed; Product; Algebras

This project is mathematical research in the theory of operator algebras. These objects turn up in some formulations of quantum mechanics, where they (or rather their selfadjoint part) represent the observables of the system being modeled. One of the basic constructions in this area is the formation of the crossed product from a group action on a given algebra. (In physics, the group would most likely be the real numbers, acting on the algebra of observables by time translation to give the dynamics of the system.) Recently, a dual construction called the crossed coproduct has turned out to be very useful, especially when the group in question is nonabelian. Professor Gootman will continue his investigations of crossed products and coproducts, particularly with an eye to studying various properties of these algebras (ideal structure, dual topology, type, etc.) by interrelating the use of non- commutative duality theory, non-abelian harmonic analysis, and representation theory.

本项目是关于数学理论的研究， 算子代数 这些物体出现在一些公式中， 量子力学，在那里它们（或者更确切地说，它们的自伴部分） 表示被建模的系统的可观测量。 之一 这一地区的基本建设是形成 在给定代数上的群作用的交叉积。 （在 在物理学中，这组数字很可能是真实的数字， 通过时间平移的观测量的代数， 系统的动态）。 最近，一个名为 交叉的余积被证明是非常有用的， 特别是当所讨论的组是非阿贝尔时。 古特曼教授将继续研究 交叉产品和副产品，特别是着眼于 研究这些代数的各种性质（理想结构， 双拓扑、类型等）通过将非- 交换对偶理论，非交换调和分析， 表征理论