Alonso Álvarez, José NicanorFernández Vilaboa, José ManuelGonzález Rodríguez, Ramón2018-11-022018-11-022017Alonso Alvarez, J.N., Fernandez Vilaboa, J.M. and Gonzalez Rodriguez, R. (2017). H-Galois extensions with normal basis for weak Hopf algebras. International Electronic Journal of Algebra, vol. 21, pp. 23-38http://hdl.handle.net/10347/17665Let 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 ϕAHeng© 2017 The Author(s). Published by IEJA. This is an open access article under under the CC-BY licenseAtribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/H-Galois extensionsNormal basisWeak Hopf algebrajournal article1306-6048open access