Mathematical Sciences: Research in Ring Theory

数学科学：环理论研究

• 批准号: 9622876
• 负责人: Kenneth Goodearl
• 金额: --
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622876&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Ring; Theory

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.

9622876本奖项支持K. Goodearl教授在非交换环理论方面的研究工作，特别强调量子群理论引起的问题。特别是，Goodearl教授将继续研究量子群与可解李代数的包络代数之间的类比，重点研究非单位根情况。这是代数子领域的研究，叫做非交换环理论。代数可以被认为是对抽象对称的研究。因此，代数在物理和化学领域有直接的应用。事实上，许多非交换环理论推广了量子力学中发现的结构，而这一提议继续探索与现代量子场论直接相关的领域。