代数群的扩展

L’Enseignement Mathématique Pub Date : 2019-07-29 DOI:10.4171/lem/65-3/4-5

M. Florence, G. Arteche

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引用次数: 0

摘要

我们将抽象群的扩展的一个经典结果推广到代数群的环境中，将$G$被$H$扩展的同构类集与$G$被$H$的中心$Z$扩展的同构类集联系起来。证明应该很容易推广到其他情况。我们还研究了分裂扩展类的子集，并通过证明这些集合在有限域上的有限性结果给出了一个快速的应用。

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On extensions of algebraic groups

We extend to the context of algebraic groups a classic result on extensions of abstract groups relating the set of isomorphism classes of extensions of $G$ by $H$ with that of extensions of $G$ by the center $Z$ of $H$. The proof should be easily generalizable to other contexts. We also study the subset of classes of split extensions and give a quick application by proving a finiteness result on these sets over a finite field.

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L’Enseignement Mathématique

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