每个霍普夫-伽罗瓦对应关系都是双射的类型分类

IF 0.8 2区 数学 Q2 MATHEMATICS
Lorenzo Stefanello , Cindy Tsang Sin Yi
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引用次数: 0

摘要

让 L/K 是任何具有伽罗瓦群 G 的有限伽罗瓦扩展。Chase 和 Sweedler 已知,对于 L/K 上的每一个 Hopf-Galois 结构,Hopf-Galois 对应都是注入式的,但在一般情况下不一定是双射的。众所周知,Hopf-Galois 结构与斜撑相关,最近,第一作者和 Trappeniers 提出了这一联系的新版本,其性质是在 Hopf-Galois 对应的映像中,L/K 的中间域与相关斜撑的左理想是双射的。作为一种应用,他们对任何 G-Galois 扩展上的每个 Hopf-Galois 结构的 Hopf-Galois 对应都是双射的群 G 进行了分类。在本文中,我们将采用类似的方法,对 N 群进行分类,对于这些群,在任何伽罗瓦扩展上的每一个 N 型 Hopf-Galois 结构,Hopf-Galois 对应都是双射的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Classification of the types for which every Hopf–Galois correspondence is bijective
Let L/K be any finite Galois extension with Galois group G. It is known by Chase and Sweedler that the Hopf–Galois correspondence is injective for every Hopf–Galois structure on L/K, but it need not be bijective in general. Hopf–Galois structures are known to be related to skew braces, and recently, the first-named author and Trappeniers proposed a new version of this connection with the property that the intermediate fields of L/K in the image of the Hopf–Galois correspondence are in bijection with the left ideals of the associated skew brace. As an application, they classified the groups G for which the Hopf–Galois correspondence is bijective for every Hopf–Galois structure on any G-Galois extension. In this paper, using a similar approach, we shall classify the groups N for which the Hopf–Galois correspondence is bijective for every Hopf–Galois structure of type N on any Galois extension.
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来源期刊
Journal of Algebra
Journal of Algebra 数学-数学
CiteScore
1.50
自引率
22.20%
发文量
414
审稿时长
2-4 weeks
期刊介绍: The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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