Induced Hopf Galois structures and their local Hopf Galois modules

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2022Embargo end date: 01 Jan 2019 Spain English Publisher:Universitat Autonoma de BarcelonaJournal:Publicacions Matemàtiques, volume 66, pages 99-128 (issn: 0214-1493,

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Authors: Daniel Gil-Muñoz; Anna Rio;

doi: 10.5565/publmat6612204 , 10.48550/arxiv.1910.06083

arXiv: 1910.06083

handle: 2117/366323

Induced Hopf Galois structures and their local Hopf Galois modules

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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.

Country

Spain

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
Universitat Politècnica de Catalunya
Spain
Autonomous University of Barcelona
Spain

Keywords

11R33, 16T05, Hopf galois structure, Field theory (Physics), :11 Number theory::11R Algebraic number theory: global fields [Classificació AMS], :Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis [Àrees temàtiques de la UPC], Classificació AMS::12 Field theory and polynomials::12F Field extensions, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis, :12 Field theory and polynomials::12F Field extensions [Classificació AMS], Teoria algebraica de, Hopf galois module theory, Nombres, Algebraic number theory, Nombres, Teoria algebraica de, FOS: Mathematics, Number Theory (math.NT), associated order, :Matemàtiques i estadística::Àlgebra::Teoria de nombres [Àrees temàtiques de la UPC], Teoria de camps (física), Classificació AMS::11 Number theory::11R Algebraic number theory: global fields, Hopf algebras and their applications, Mathematics - Number Theory, Hopf Galois module theory, Hopf Galois structure, Associated order, Integral representations related to algebraic numbers; Galois module structure of rings of integers, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres

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