Mathematical Sciences: Group Rings and Enveloping Algebras

该奖项涉及非交换环理论的两个领域的研究。首席研究员将研究群代数的半原性。主要目标是研究局部有限的情况，以及更困难的有限生成情况的某些方面。此外，他将致力于开发彩色李代数包络代数中的δ方法，并理解有限维Hopf代数的h -伽罗瓦作用与这些Hopf代数的不可约表示之间的关系。最后，他计划研究量子包络代数，看看包络代数的方法是否可以扩展到这些环的性质，这些性质不遵循通常的诺etherian技术。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。

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.