Mathematical Sciences: Sklyanin Algebras, and Graded Algebras

本研究关注的是对新一类 分次代数，包括Sklyanin代数，正则代数和 与量子群有关的代数。目标是了解他们的 用几何术语表示理论。 校长 研究人员将研究有限维简单模块的 Sklyanin代数 他将检查更高维度的Sklyanin 正则性和诺特链等性质的代数 条件 他还将从一个 变形透视 本文的研究是在非交换环的一般范畴内进行的 理论 该项目中考虑的环是感兴趣的， 包括代数几何在内的许多数学领域。 给予 曲线，其中一个环可以与曲线上的某些点相关联。 曲线。 更好地理解这些环和这个 关联将有助于确定给定的 曲线

This research is concerned with the study of new classes of graded algebras including Sklyanin algebras, regular algebras and algebras related to quantum groups. The goal is to understand their representation theory in geometric terms. The principal investigator will study the finite dimensional simple modules of Sklyanin algebras. He will examine higher dimensional Sklyanin algebras for properties such as regularity and noetherian chain conditions. He will also examine their properties from a deformation perspective. This research is in the general area of noncommutative ring theory. The rings considered in the project are of interest in many areas of mathematics including algebraic geometry. Given a curve, one of these rings can be associated with certain points on the curve. A better understanding of these rings and this association will be useful in determining the geometry of a given curve.