On Galois extension of Hopf algebras

Abstract

Let H be a cosemisimple Hopf algebra over a field k, and π: A → H be a surjective cocentral bialgebra homomorphism of bialgebras. The authors prove that if A is Galois over its coinvariants B = LH Ker π and B is a sub-Hopf algebra of A, then A is itself a Hopf algebra. This generalizes a result of Cegarra [3] on group-graded algebras.

Keywords

Hopf algebra / Galois extension

References

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