Mathematical Sciences: Group Rings and Enveloping Algebras

点击翻译按钮获取中文摘要

This award is concerned with research in two areas of noncommutative ring theory. The principal investigator will study the semiprimitivity of group algebras. The main goal is to work on the locally finite case and on some aspects of the more difficult finitely generated case. In addition, he will work on developing delta methods in enveloping algebras of color Lie algebras and on understanding the relationship between H-Galois actions of finite dimensional Hopf algebras and the irreducible representations of these Hopf algebras. Finally, he plans to work on quantum enveloping algebras to see whether the enveloping algebra delta methods can be extended to yield properties of these rings which do not follow from the usual Noetherian techniques. 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.