论文标题
线性差异方程的GALOIS组
Galois Groups of Linear Difference-Differential Equations
论文作者
论文摘要
我们研究了线性差异分辨率系统的Galois组$ g $与两个类别的galois组的galois组的线性差异方程式和线性差分方程中的galois组的两个类别的$ \ Mathcal {C} _1 $和$ \ Mathcal {C} _2 $之间的关系。我们表明，几乎所有组中的所有组中的所有组中的所有组都是$ g $的代数子组，并且有$ \ nathcal {c} _1 $的非空子集和一个非空置的$ \ rathcal iS $ \ ratscal {c $ g $ g $ g $ g $的代数{子集。这些结果潜在地应用了线性差异差异系统的Galois组的计算。我们还提供了一个标准，用于在简单的差异环中测试元素的线性依赖性，该环概括了Kolchin的部分差分字段的标准。
We study the relation between the Galois group $G$ of a linear difference-differential system and two classes $\mathcal{C}_1$ and $\mathcal{C}_2$ of groups that are the Galois groups of the specializations of the linear difference equation and the linear differential equation in this system respectively. We show that almost all groups in $\mathcal{C}_1\cup \mathcal{C}_2$ are algebraic subgroups of $G$, and there is a nonempty subset of $\mathcal{C}_1$ and a nonempty subset of $\mathcal{C}_2$ such that $G$ is the product of any pair of groups from these two subsets. These results have potential application to the computation of the Galois group of a linear difference-differential system. We also give a criterion for testing linear dependence of elements in a simple difference-differential ring, which generalizes Kolchin's criterion for partial differential fields.
