Mathematical Sciences: Noncommutative Algebras

数学科学：非交换代数

• 批准号: 8901873
• 负责人: Marvin Wunderlich
• 金额: --
• 依托单位: National Security Agency
• 依托单位国家: 美国
• 项目类别: Interagency Agreement
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901873&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Noncommutative; Algebras

This research is concerned with the structure of certain noncommutative algebras. The main concern is the structure of algebras which arise as deformations of fixed rings of the Weyl algebras. The techniques used to study these algebras involve the intertwining of ideas from the theory of Lie algebras and algebraic geometry. The principle investigator will also pursue the study of enveloping algebras, focusing on the problem of calculating the K-theory of primitive factors of the enveloping algebra of a semi-simple Lie algebra. Noncommutative ring theory represents the study of an algebraic structure possessing an addition and a noncommutative multiplication. K-theory represents the evolved algebraic theory of vector spaces and linear mappings. This project is concerned with the structure, K-theory and state-space of certain noncommutative rings.

本文主要研究一类非交换代数的结构。主要关注的是结构的代数出现的变形固定环的Weyl代数。用于研究这些代数的技术涉及李代数理论和代数几何的思想交织。主要研究者还将从事包络代数的研究，重点研究计算半单李代数的包络代数的本原因子K理论的问题。非交换环理论研究的是具有加法和非交换乘法的代数结构。K-理论代表向量空间和线性映射的演化代数理论。这个项目关注的是某些非交换环的结构、K-理论和状态空间。