Mathematical Sciences: Group Rings and Related Algebras

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9622566 Passman This award supports the research of Professor D. Passman to work in non-commutative ring theory. He intends to study the semiprimitivity conjecture for group rings. He also wants to work on the ideal structure of certain group algebras. He also hopes to understand better the relation between H-Galois actions on Hopf algebras and their irreducible representations. Finally, he intends to study delta methods in quantum enveloping algebras. This is research in the subfield of algebra called non-commutative ring theory. Algebra can be thought of as the study of symmetry in the abstract. As such, algebra has direct applications to areas of physics and chemistry. In fact, much of non-commutative ring theory generalizes structures found in quantum mechanics and some of these problems have possible implications for the modern theory of quantum fields.