Cohomology and Representation Theory: Algebraic Groups, Finite Groups and Lie Algebras

上同调和表示论：代数群、有限群和李代数

• 批准号: 9800960
• 负责人: Daniel Nakano
• 金额: $ 7.29万
• 依托单位: Utah State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-09-01 至 2001-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9800960&HistoricalAwards=false
• 关键词: Cohomology; Representation; Theory; Algebraic; Groups

9800960 Nakano This award supports work on problems in the representation and cohomology theory of algebraic groups and related structures. These related structures include Lie algebras, infinitesimal group schemes, quantum groups, Schur algebras, symmetric groups and Hecke algebras. Many of the problems reduce to studying the representation theory for certain finite-dimensional algebras. These algebras are in general not semisimple so the fundamental representation questions involve determining the simple and projective modules, computing the composition factors of the projective modules, understanding the block theory and classifying the indecomposable modules. The principal investigator will also work on the use of geometric methods in the representation/cohomology theory for these related structures. The research supported concerns the representation theory of various algebraic objects including algebraic groups and Lie algebras. Representation theory is an important method for determining the structure of these objects. This work has implications for a number of areas of mathematics including ring theory, group theory, topology and the study of Lie algebras.

9800960 Nakano 该奖项支持代数群及相关结构的表示和上同调理论问题的研究。 这些相关结构包括李代数、无穷小群方案、量子群、舒尔代数、对称群和赫克代数。 许多问题归结为研究某些有限维代数的表示论。 这些代数通常不是半简单的，因此基本的表示问题涉及确定简单模和射影模、计算射影模的组成因子、理解分块理论以及对不可分解模进行分类。 首席研究员还将致力于在这些相关结构的表示/上同调理论中使用几何方法。 支持的研究涉及各种代数对象的表示论，包括代数群和李代数。 表示论是确定这些对象结构的重要方法。 这项工作对许多数学领域都有影响，包括环论、群论、拓扑和李代数的研究。