Truman, PJ, Koch, A, Kohl, T and Underwood, R (2018) Isomorphism problems for Hopf-Galois structures on separable field extensions. Journal of Pure and Applied Algebra. ISSN 0022-4049 (In Press)

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Abstract

Let L=K be a finite separable extension of fields whose Galois closure E=K has Galois group G. Greither and Pareigis use Galois descent to show that a Hopf algebra giving a Hopf-Galois structure on L=K has the form E[N]G for some group N of order [L : K]. We formulate criteria for two such Hopf algebras to be isomorphic as Hopf algebras, and provide a variety of examples. In the case that the Hopf algebras in question are commutative, we also determine criteria for them to be isomorphic as K-algebras. By applying our results, we complete a detailed analysis of the distinct Hopf algebras and K-algebras that appear in the classification of Hopf-Galois structures on a cyclic extension of degree pn, for p an odd prime number.

Item Type: Article
Additional Information: This is the accepted author manuscript (AAM). The final published version (version of record) will be available online via Elsevier at https://www.sciencedirect.com/journal/journal-of-pure-and-applied-algebra - please refer to any applicable terms of use of the publisher.
Uncontrolled Keywords: Hopf-Galois extension, Greither-Pareigis theory, Galois descent, 2000 MSC: 16T05
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Maths
Depositing User: Symplectic
Date Deposited: 05 Jul 2018 10:46
Last Modified: 05 Jul 2018 10:47
URI: http://eprints.keele.ac.uk/id/eprint/5096

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