Mathematical Sciences: Modular Representations of Finite Groups

数学科学：有限群的模表示

• 批准号: 9301929
• 负责人: Jon Carlson
• 金额: $ 24.49万
• 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: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301929&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Modular; Representations; Finite

This award is concerned with the representation theory and cohomology of finite groups over fields of prime characteristic. Of particular interest are the homological properties of representations which underlie the basic module theory and the structure of the cohomology ring of the group which acts on the fundamental homological constructions. The principal investigator plans to study the prime ideals which are the annihilators of cohomology elements and their relations to transfers from and restrictions to subgroups of the group. Categorical techniques, as well as hypercohomology spectral sequences associated to certain duality complexes and actions of the Steenrod algebra, will be used for this investigation. Other questions on the structure of modules in the more general categorical setting will also be examined. In addition, the principal investigator will continue work on the homological algebra of Hilbert modules and on computer methods for the computation of cohomology. The research supported concerns the representation theory of finite groups. A group is an algebraic object used to study transformations. Because of this, groups are a fundamental tool in physics, chemistry and computer science as well as mathematics. Representation theory is an important method for determining the structure of groups.

该奖项涉及素特征域上有限群的表示理论和上同调。特别令人感兴趣的是表示的同调性质，它是基本模理论和作用于基本同调结构的群的上同调环的结构的基础。主要研究者计划研究素理想，它们是上同调元素的零化子，以及它们与群的子群的转移和限制的关系。分类技术，以及与某些对偶复合体和Steenrod代数的作用有关的超上同调谱序列，将被用于这一研究。在更一般的分类背景下，还将考察有关模块结构的其他问题。此外，主要研究人员将继续研究Hilbert模的同调代数和计算上同调的计算机方法。所支持的研究涉及有限群的表示理论。群是用于研究变换的代数对象。正因为如此，小组是物理、化学和计算机科学以及数学中的基本工具。表象理论是确定群结构的重要方法。