H-Galois extensions with normal basis for weak Hopf algebras
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Title: | H-Galois extensions with normal basis for weak Hopf algebras |
Author: | Alonso Álvarez, José Nicanor Fernández Vilaboa, José Manuel González Rodríguez, Ramón |
Affiliation: | Universidade de Santiago de Compostela. Departamento de Matemáticas |
Subject: | H-Galois extensions | Normal basis | Weak Hopf algebra | |
Date of Issue: | 2017 |
Publisher: | International Electronic Journal of Algebra |
Citation: | Alonso 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. 23-38 |
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 |
URI: | http://hdl.handle.net/10347/17665 |
E-ISSN: | 1306-6048 |
Rights: | © 2017 The Author(s). Published by IEJA. This is an open access article under under the CC-BY license Atribución 4.0 Internacional |
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