Mathematical Sciences: Noncommutative Projective Geometry

本研究涉及非交换代数， 特别是非交换Noether环的理论， 它的应用到其他数学领域。 校长 研究者将研究非平凡的抽象性质 例子及其与量子理论的相互关系 组 他还将考虑有限的斜群环 群作用在多项式环上，以确定当范畴 环上的投射模满足消去。 博士后助理将研究的稳定排名 半单李代数的包络代数 一个环是一个代数对象，它既有加法又有 乘法定义。虽然加法运算 满足交换律，乘法运算是 不需要这样做。 非交换环的研究 由于代数的不断增加，成为代数的重要组成部分 对数学和物理学的其他分支具有重要意义。

This research is concerned with noncommutative algebra, particularly the theory of noncommutative noetherian rings and its applications to other areas of mathematics. The principal investigator will study the abstract properties of nontrivial examples and their interrelationship with the theory of quantum groups. He will also consider the skew group ring of a finite group acting on a polynomial ring to determine when the category of projective modules over such a ring satisfies cancellation. The postdoctoral associate will study the stable rank of enveloping algebras of semisimple Lie algebras. 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. The study of noncommutative rings has become an important part of algebra because of its increasing significance to other branches of mathematics and physics.