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arXiv · 1403.6300

From Galois to Hopf Galois: theory and practice

Teresa Crespo·Anna Rio·Montserrat Vela
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Abstract

Hopf Galois theory expands the classical Galois theory by considering the Galois property in terms of the action of the group algebra k[G] on K/k and then replacing it by the action of a Hopf algebra. We review the case of separable extensions where the Hopf Galois property admits a group-theoretical formulation suitable for counting and classifying, and also to perform explicit computations and explicit descriptions of all the ingredients involved in a Hopf Galois structure. At the end we give just a glimpse of how this theory is used in the context of Galois module theory for wildly ramified extensions.

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Teresa Crespo, Anna Rio, Montserrat Vela. 2014-03-25. From Galois to Hopf Galois: theory and practice. https://arxiv.org/abs/1403.6300

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