Mathematical Sciences: Hopf Algebras and Their Actions on Rings

主要研究者将调查 环上的Hopf代数，特别是交叉积和内环 行动 的操作的早期结果 群作为自同构，李代数作为导子。 其他问题涉及到Weyl代数何时可以是一个固定环， 研究了量子包络的余代数结构 代数 博士后助理将致力于量子群 和拟三角Hopf代数 她还将考虑 一般Hopf代数及其在H-模代数上的作用 这项研究是在环理论的一般领域。 的环 是一个既有加法又有乘法的代数对象， 尽管加法运算满足 交换律，不需要乘法运算 这样做. 一个环的例子，其中乘法不是 交换的是整数上的nxn矩阵的集合。 对非交换环的研究已经成为环理论的一个重要组成部分， 代数，因为它对其他分支的重要性越来越大 数学和物理学。

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.