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

H-GALOIS EXTENSIONS WITH NORMAL BASIS FOR WEAK HOPF ALGEBRAS

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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International Electronic Journal of Algebra-Cover

ISSN: 1306-6048
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2007
Yayıncı: Abdullah HARMANCI

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