H-GALOIS EXTENSIONS WITH NORMAL BASIS FOR WEAK HOPF ALGEBRAS

Year 2017, Volume: 21 Issue: 21, 23 - 38, 17.01.2017

J. N. Alonso Alvarez J. M. Fernandez Vilaboa R. Gonzalez Rodriıguez

https://doi.org/10.24330/ieja.295749

Abstract

 Let H be a weak Hopf algebra and let A be an H-comodule algebra
with subalgebra of coinvariants AH. In this paper we introduce the
notion of H-Galois extension with normal basis and we prove that AH ,→ A
is an H-Galois extension with normal basis if and only if AH ,→ A is an
H-cleft extension which admits a convolution invertible total integral. As a
consequence, if H is cocommutative and A commutative, we obtain a bijective
correspondence between the second cohomology group H2
ϕAH
(H, AH) and the
set of isomorphism classes of H-Galois extensions with normal basis whose left
action over AH is ϕAH . 

Keywords

H-Galois extensions, normal basis

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