H-GALOIS EXTENSIONS WITH NORMAL BASIS FOR WEAK HOPF ALGEBRAS

Authors : J N Alonso Alvarez, J M Fernandez Vilaboa, R Gonzalez Rodriıguez

Pages : 23-38

Doi:10.24330/ieja.295749

View : 17 | Download : 15

Publication Date : 2017-01-17

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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