Mathematical Sciences: Research in Ring Theory

9622876 该奖项支持K教授的研究。致力于非交换环理论的研究，特别强调量子群理论所产生的问题。特别是，教授Goodearl将继续调查之间的类比量子群和包络代数的可解李代数集中在非根的统一情况。 这是在代数的一个子领域的研究，叫做非交换环理论。代数学可以看作是抽象的对称性研究。因此，代数直接应用于物理和化学领域。事实上，许多非对易环理论概括了量子力学中发现的结构，并且该提议继续探索与现代量子场论直接相关的领域。

9622876 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.