Modular Representations of Finite Groups

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CARLSON, 98-70035The project is an investigation into the representation theory and cohomology of finite groups over fields of finite characteristic. Of particular interest are the homological properties of representations which underline the basic module theory, and the structure of the cohomology ring of the group which acts on the fundamental homological constructions. The proposer plans to continue his development of computer algebra systems for experimentation with modules, homomorphisms and group cohomology.The field of group theory is the mathematical theory of symmetry and interacts with many other disciplines, for example physics and chemistry outside of mathematics, coding theory, number theory and geometry inside mathematics. The investigator's particular area is a meld of representation theory, homological algebra and the use of computer techniques.