Mathematical Sciences: Modular Representations of Finite Groups

这个奖项是关于素数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构成基本模理论基础的表示的同调性质，以及作用于基本同调构造的群的上同调环的结构。主要研究上同元湮灭子的素理想及其与群的子群迁移和子群约束的关系。分类技术，以及与某些对偶配合物和Steenrod代数的作用相关的超上同调谱序列，将用于这项研究。在更一般的分类设置模块结构的其他问题也将审查。此外，首席研究员将继续研究Hilbert模的同调代数和计算上同调的计算机方法。本研究支持有限群的表示理论。群是用来研究变换的代数对象。正因为如此，分组是物理、化学、计算机科学以及数学的基本工具。表征理论是确定群体结构的重要方法。

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.