论文标题
可分离场扩展上的最小Hopf-Galois结构
Minimal Hopf-Galois Structures on Separable Field Extensions
论文作者
论文摘要
在Hopf-Galois理论中，场扩展上的每$ H $ -HOPF-GALOIS结构$ k/k $都会从$ k $ -sub-sub-hopf代数$ h $ of $ k/k/k $的中间字段中产生$ k $ -sub-sub-hopf $ h $ $ h $的注入性映射$ \ mathcal {f} $。关于$ \ Mathcal {f} $过滤性失败的最新论文表明，存在许多Hopf-Galois结构，其子场比子-HOPF代数多。本文调查并说明了群体理论方法，以确定在极端情况下$ h $ -HOPF-GALOIS结构在有限的可分离扩展中，而$ H $只有两个子-HOPF代数。
In Hopf-Galois theory, every $H$-Hopf-Galois structure on a field extension $K/k$ gives rise to an injective map $\mathcal{F}$ from the set of $k$-sub-Hopf algebras of $H$ into the intermediate fields of $K/k$. Recent papers on the failure of the surjectivity of $\mathcal{F}$ reveal that there exist many Hopf-Galois structures for which there are many more subfields than sub-Hopf algebras. This paper surveys and illustrates group-theoretical methods to determine $H$-Hopf-Galois structures on finite separable extensions in the extreme situation when $H$ has only two sub-Hopf algebras.
