Mathematical Sciences: Group Actions on Rings

主要研究人员将研究群在各种环境下在非对易环上的作用。特别是，他将研究Tori和其他代数群在多项式单位代数上的作用。本研究属于环论的一般领域。环是定义了加法和乘法的代数对象。虽然加法运算满足交换律，但乘法运算不是必须的。乘法不可交换的环的一个例子是整数上的n×n矩阵的集合。非对易环的研究已经成为代数的重要组成部分，因为它对数学和物理的其他分支的意义越来越大。

The principal investigator will study actions of groups on noncommutative rings in various settings. In particular, he will investigate actions of tori and other algebraic groups on polynomial identity algebras. This research is in the general area of ring theory. A ring is an algebraic object having both an addition and a multiplication 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.