Mathematical Sciences: Finite Dimensional Simple Modules andPrimitive Ideals

数学科学：有限维简单模和原理想

• 批准号: 8901890
• 负责人: S. Paul Smith
• 金额: $ 4.73万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901890&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Finite; Dimensional; Simple

This research is concerned with the study of new classes of noncommutative noetherian rings. An underlying goal is to show that there are many algebras which have a structure similar to the enveloping algebra of a semisimple Lie algebra. Among those to be studied are some having primitive factor rings which have an associated graded algebra which is the coordinate ring of a Kleinian singularity. In addition, the enveloping algebras of Lie superalgebras, and q-analogues of enveloping algebras will be studied with the long-term goal of classifying the space of primitive ideals. This research is in the general area of noncommutative ring theory. The rings considered in the project are of interest in many areas of mathematics including algebraic geometry. 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 determining the geometry of a given curve.

本文研究了一类新的非交换诺瑟环。一个潜在的目标是表明有许多代数具有类似于半简单李代数的包络代数的结构。在这些被研究的环中，有一些具有原始因子环，它们有一个相关联的梯度代数，即Kleinian奇点的坐标环。此外，李超代数的包络代数和包络代数的q-类似物将以对原始理想空间的分类为长期目标进行研究。本研究属于非交换环理论的一般范畴。项目中考虑的环在数学的许多领域都很有趣，包括代数几何。给定一条曲线，其中一个环可以与曲线上的某些点相关联。更好地理解这些环和它们之间的联系将有助于确定给定曲线的几何形状。