Mathematical Sciences: Representations of Lie Algebras

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9622876 Goodearl This award supports the research of Professor K. Goodearl to work in non-commutative ring theory with special emphasis on problems arising from the theory of Quantum Groups. In particular, Professor Goodearl will continue to investigate analogies between Quantum Groups and enveloping algebras of solvable Lie algebras concentrating on the non-root-of-unity case. This is research in the subfield of algebra called non-commutative ring theory. Algebra can be though 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 this proposal continues to explore areas that connect directly with modern quantum field theory. ??