Mathematical Sciences: Noncommutative Projective Geometry

这项研究涉及非交换代数，特别是非交换Notherian环的理论及其在其他数学领域的应用。主要研究人员将研究非平凡例子的抽象性质及其与量子群理论的相互关系。他还将考虑作用在多项式环上的有限群的斜群环，以确定这种环上的投射模范畴何时满足消去。博士后将研究半单李代数的包络代数的稳定秩.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。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。

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.