Mathematical Sciences: Rings of Differential Operators

设X是环上的不可约仿射代数曲线， 复数，设D（X）表示其微分环 运营商这个项目涉及到确定两个 不可约仿射曲线X和Y，当D（X）和D（Y）是 同构意味着X和Y是同构的。的途径 这个问题将涉及到找到最大的交换 D（X）的ad-nilpotent子代数，然后确定 Y的坐标环同构于一个自幂零环 D（X）的子代数意味着D（X）和D（Y）是同构的。 这个项目是在环理论的一般领域。的环 是一个带有加法和乘法的代数对象 这个特殊的项目涉及到一个 一个特殊的环叫做微分算子环， 仿射曲线这些环在以下几个方面很重要： 数学和物理。

Let X be an irreducible affine algebraic curve over the complex numbers, and let D(X) denote its ring of differential operators. This project is concerned with determining for two irreducible affine curves X and Y, when D(X) and D(Y) being isomorphic implies that X and Y are isomorphic. The approach to this problem will involve finding the maximal commutative ad-nilpotent subalgebras of D(X) and then determining if the coordinate ring of Y being isomorphic to an ad-nilpotent subalgebra of D(X) implies that D(X) and D(Y) are isomorphic. This project is in the general area of ring theory. A ring is an algebraic object with an addition and multiplication defined on it. This particular project is concerned with a special ring call the ring of differential operators of an affine curve. These rings are important in several areas of mathematics and physics.