Mathematical Sciences: Enveloping Superalgebras, Quantum Groups, and Their Prime Ideals

该奖项涉及对某些结合代数的内部结构和表示理论的研究，这些结合代数是当前数学物理和李表示理论中的研究热点，即李超代数的量子群和包络代数。要研究的量子群是代数群的量子化坐标环；要考虑的李超代数是经典的简单可解的李超代数。全文的重点将放在素数和本原理想理论上，原理方法涉及环扩张的新归纳技术。量子群对数学家和物理学家来说都是一个新的研究领域。在数学方面，它结合了代数、分析和几何这三个最古老的纯数学领域，但它对致力于共形量子场论的物理学家非常感兴趣。

This award is concerned with research into the internal structure and representation theory of certain associative algebras that are of current interest within mathematical physics and Lie representation theory, namely quantum groups and enveloping algebras of Lie superalgebras. The quantum groups to be studied are the quantized coordinate rings of algebraic groups; the Lie superalgebras which will be considered are the classical simple and solvable ones. The focus throughout will be on prime and primitive ideal theory, and the principle methods involve new induction techniques for ring extensions. Quantum groups are a new area of research for both mathematicians and physicists. On the mathematical side, it combines three of the oldest areas of "pure" mathematics, algebra, analysis and geometry, yet it is of great interest to physicists working on conformal quantum field theory.