Mathematical Sciences: Hopf Algebras and Their Actions on Rings

数学科学：Hopf 代数及其对环的作用

• 批准号: 9203375
• 负责人: Susan Montgomery
• 金额: $ 19.64万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203375&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Hopf; Algebras; Their

The principal investigator will investigate the actions of Hopf algebras on rings, in particular crossed products and inner actions. The object is to extend earlier results for actions of groups as automorphisms and of Lie algebras as derivations. Other problems concern when the Weyl algebra can be a fixed ring, and studying the coalgebra structure of the quantum enveloping algebras. The postdoctoral associate will work on quantum groups and quasitriangular Hopf algebras. She will also consider general Hopf algebras and their actions on H-module algebras. This research is in the general area of ring theory. A ring is an algebraic object having both an addition and a multiplica- tion defined on it. Although the additive operation satisfies the commutative law, the multiplicative operation is not required to do so. An example of a ring for which multiplication is not commutative is the collection of nxn matrices over the integers. The study of noncommutative rings has become an important part of algebra because of its increasing significance to other branches of mathematics and physics.

首席研究员将研究Hopf代数在环上的作用，特别是交叉积和内作用。目的是推广先前关于群的自同构作用和李代数的派生作用的结果。其他问题涉及Weyl代数何时可以是一个固定环，以及研究量子包络代数的协代数结构。该博士后将研究量子群和拟三角形霍普夫代数。她还将考虑一般的Hopf代数及其对h模代数的作用。本研究属于环理论的一般范畴。环是一个代数对象，在它上面定义了加法和乘法。虽然加法运算满足交换律，但乘法运算不需要满足交换律。一个乘法不可交换的环的例子是整数上的nxn个矩阵的集合。非交换环的研究由于其对其他数学和物理分支的重要意义而成为代数的重要组成部分。