Extensions finites Hopf Galois

Abstract

[en] Galois theory is one of the most famous in the mathematics field. This theory usually uses groups as the main structure of study. We’ll work to find a generalization of this theory, which will consist of using a more complex structure, the Hopf algebra. In the end, we’ll be able to find a relationship between a Hopf algebra associated with a Hopf Galois extension and a regular subgroup of permutations. This final result will be the one that will enable us to explicitly compute a Hopf algebra given the regular subgroup.