Mathematical Sciences: Modular Representations of Finite Groups

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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.