论文标题
在差异galois理论中的经典群体的一般扩展字段上
On General Extension Fields for the Classical Groups in Differential Galois Theory
论文作者
论文摘要
让$ g $是谎言排名$ l $的古典群体之一。我们像E. Noether在有限群体的古典Galois理论中一样，在差异Galois理论中使用差异性Galois理论的一般扩展领域进行类似的结构。更确切地说，我们建立了一个差异性超越程度$ l $ $ l $的差异字段，而$ g $ ACT的常数并表明它是不变式$ e^g $领域的Picard-vessiot扩展。 $ l $差异多项式在差异上产生了字段$ e^g $，这些多项式在代数上独立于常数。它们是扩展方程的系数。最后，我们证明我们的构造满足了特定类型的$ g $ PICARD-PICARD-PESSIOT扩展的通用属性。
Let $G$ be one of the classical groups of Lie rank $l$. We make a similar construction of a general extension field in differential Galois theory for $G$ as E. Noether did in classical Galois theory for finite groups. More precisely, we build a differential field $E$ of differential transcendence degree $l$ over the constants on which the group $G$ acts and show that it is a Picard-Vessiot extension of the field of invariants $E^G$. The field $E^G$ is differentially generated by $l$ differential polynomials which are differentially algebraically independent over the constants. They are the coefficients of the defining equation of the extension. Finally we show that our construction satisfies generic properties for a specific kind of $G$-primitive Picard-Vessiot extensions.
