Induced Hopf Galois structures and their local Hopf Galois modules
The regular subgroup determining an induced Hopf Galois structure for a Galois extension L/K is obtained as direct product of the corresponding regular groups of the inducing subextensions. We describe here the attached Hopf algebra and Hopf action of an induced structure and we prove that they are...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/366323 |
| Acceso en línea: | https://hdl.handle.net/2117/366323 https://dx.doi.org/10.5565/PUBLMAT6612204 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebraic number theory Field theory (Physics) Hopf Galois structure Hopf Galois module theory Associated order Nombres, Teoria algebraica de Teoria de camps (física) Classificació AMS::11 Number theory::11R Algebraic number theory: global fields Classificació AMS::12 Field theory and polynomials::12F Field extensions Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis |
| Sumario: | The regular subgroup determining an induced Hopf Galois structure for a Galois extension L/K is obtained as direct product of the corresponding regular groups of the inducing subextensions. We describe here the attached Hopf algebra and Hopf action of an induced structure and we prove that they are obtained by tensoring the corresponding inducing objects. We give a general matrix description of the Hopf action which is useful to compute bases of associated orders. In case of an induced Hopf Galois structures it allows us to decompose the associated order, assuming that inducing subextensions are arithmetically disjoint. |
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