Induced Hopf Galois structures and their local Hopf Galois modules

Pub Date : 2019-10-14 DOI:10.5565/PUBLMAT6612204
Daniel Gil-Muñoz, A. Rio
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引用次数: 4

Abstract

The regular subgroup determining an induced Hopf Galois structure for a Galois extension $L/K$ is obtained as the direct product of the corresponding regular groups of the inducing subextensions. We describe here the associated Hopf algebra and Hopf action of an induced structure and we prove that they are obtained by tensoring the corresponding inducing objects. In order to deal with their associated orders we develop a general method to compute bases and free generators in terms of matrices coming from representation theory of Hopf modules. In the case of an induced Hopf Galois structure it allows us to decompose the associated order, assuming that inducing subextensions are arithmetically disjoint.
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诱导Hopf伽罗瓦结构及其局部Hopf伽罗瓦模块
作为诱导子扩展对应正则群的直接积,得到了确定伽罗瓦扩展L/K的诱导Hopf伽罗瓦结构的正则子群。本文描述了诱导结构的Hopf代数和Hopf作用,并证明了它们是通过张紧相应的诱导对象得到的。为了处理它们的关联阶,我们从Hopf模的表示理论出发,提出了一种用矩阵计算基和自由发生器的一般方法。在诱导Hopf伽罗瓦结构的情况下,它允许我们分解相关的顺序,假设诱导子扩展在算术上是不相交的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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