Mathematical Sciences: Actions of Groups and Hopf Algebras

本课题研究非交换环上有限群作用的理论。首席研究员将研究环的自同构群，以及更一般的霍普夫代数的作用。具体的题目包括素环的广义Picard群以及歪斜群环为素的条件。该博士后将研究代数群在结合代数上的作用。这个项目属于环理论的一般领域。环是一个代数对象，在它上面定义了加法和乘法。环在物理学和计算机科学以及数学的许多分支中都很有趣。

This project is concerned with the theory of finite group actions on noncommutative rings. The principal investigator will study automorphism groups of rings, and more generally the actions of Hopf algebras. The specific topics include a generalized Picard group for prime rings as well as conditions for the skew group ring to be prime. The postdoctoral associate will study actions of algebraic groups on associative algebras. This project is in the general area of ring theory. A ring is an algebraic object having both an addition and a multiplication defined on it. Rings are of interest in physics and computer science as well as many branches of mathematics.