Mathematical Sciences: Rings of Differential Operators and Enveloping Algebras

数学科学：微分算子环和包络代数

• 批准号: 8702447
• 负责人: S. Paul Smith
• 金额: $ 4.31万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702447&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Rings; Differential; Operators

This research will focus on the study of differential operators on algebraic varieties and the connections with primitive ideals in the enveloping algebra of a semi-simple Lie algebra. Given a curve, there is a finite dimensional algebra (a certain factor ring of the ring of differential operators) associated to each singular point of the curve. A general problem is to understand the precise relation between the local geometry at a singular point, and the structure of the ring of differential operators. This research is in the general area of noncommutative ring theory. The rings considered in this project are of great interest in many parts of mathematics. Given a curve, one of these rings can be associated with certain points on the curve. A better understanding of these rings and this association will be useful in determing the geometry of a given curve.

本研究将重点研究代数簇上的微分算子以及半单李代数的包络代数中与本原理想的联系。给定一条曲线，有一个与曲线的每个奇异点相关联的有限维代数（微分算子环的某个因子环）。一个普遍的问题是理解奇点处的局部几何与微分算子环的结构之间的精确关系。 这项研究属于非交换环理论的一般领域。 该项目中考虑的环在数学的许多部分都引起了极大的兴趣。 给定一条曲线，这些环之一可以与曲线上的某些点相关联。 更好地理解这些环和这种关联将有助于确定给定曲线的几何形状。