Translator Disclaimer
2022 Induced Hopf Galois structures and their local Hopf Galois modules
Daniel Gil-Muñoz, Anna Rio
Author Affiliations +
Publ. Mat. 66(1): 99-128 (2022). DOI: 10.5565/PUBLMAT6612204

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 this allows us to decompose the associated order, assuming that inducing subextensions are arithmetically disjoint.

Citation

Download Citation

Daniel Gil-Muñoz. Anna Rio. "Induced Hopf Galois structures and their local Hopf Galois modules." Publ. Mat. 66 (1) 99 - 128, 2022. https://doi.org/10.5565/PUBLMAT6612204

Information

Received: 18 February 2020; Accepted: 17 September 2020; Published: 2022
First available in Project Euclid: 4 January 2022

Digital Object Identifier: 10.5565/PUBLMAT6612204

Subjects:
Primary: 11R33 , 16T05

Keywords: associated order , Hopf Galois module theory , Hopf Galois structure

Rights: Copyright © 2022 Universitat Autònoma de Barcelona, Departament de Matemàtiques

JOURNAL ARTICLE
30 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.66 • No. 1 • 2022
Back to Top