Mathematical Sciences: Groups and Rings

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This project is concerned with research in group theory and ring theory. One investigator will be working on character theory. In particular, he will examine M-groups, the properties of the set of irreducible character degrees of solvable groups and the interactions between characters and sets of primes in these groups. The other investigator will work on group rings, crossed products, Galois theory and enveloping rings. He will apply Delta-methods to restricted enveloping rings of infinite dimensional Lie algebras. He will also determine when such rings satisfy a polynomial identity. Furthermore he plans to work on computations of Grothendieck groups and Gelfand-Kirilov dimension. A group is an algebraic structure with one operation. A ring is an algebraic structure with two operations, addition and multiplication. It forms a group with respect to addition. These are basic abstract structures which occur in many settings in mathematics, chemistry and physics.