Mathematical Sciences: Linear Groups Over Fields Generated by Nilpotent Group Rings and Enveloping Algebras

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This project is concerned with the study of linear groups over fields of fractions of enveloping algebras and polycyclic groups rings. The principal investigator will extend known results from ordinary linear group theory to linear groups over the noncommutative division rings which arise from enveloping algebras of Lie algebras and from group rings of polycyclic groups. Certain related ring theoretic problems such as what are the finite dimensional algebras will also be considered. This research focuses on the study of matrix rings over fields of fractions. Little is known about the structure of algebraic objects over skew fields and the principal investigator is one of the few researchers who is trying to improve this situation.