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| Crossed Products over Weak Hopf Algebras Related toCleft Extensions and Cohomology? |
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Citation： |
Jos´e Nicanor Alonso ´ALVAREZ1 Jos´e Manue,Fern´andez VILABOA,Ram´on Gonz´alez RODR´IGUEZ.Crossed Products over Weak Hopf Algebras Related toCleft Extensions and Cohomology?[J].Chinese Annals of Mathematics B,2014,35(2):161~190 |
| Page view： 1973
Net amount： 1439 |
Authors： |
Jos′e Nicanor Alonso ′ALVAREZ1 Jos′e Manue; Fern′andez VILABOA; Ram′on Gonz′alez RODR′IGUEZ; |
Foundation： |
Ministerio de Ciencia e Innovaci′on (No.MTM2010-15634)and Fondo Europeo de Desarrollo Regional. |
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| Abstract： |
The authors present the general theory of cleft extensions for a cocommutative
weak Hopf algebra H. For a right H-comodule algebra, they obtain a bijective correspondence
between the isomorphisms classes of H-cleft extensions AH → A, where AH is
the subalgebra of coinvariants, and the equivalence classes of crossed systems for H over
AH. Finally, they establish a bijection between the set of equivalence classes of crossed
systems with a fixed weak H-module algebra structure and the second cohomology group H2? Z(AH) (H,Z(AH)), where Z(AH) is the center of AH. |
Keywords： |
Monoidal category, Weak Hopf algebra, Cleft extension, Weak crossedproduct, Sweedler cohomology for weak Hopf algebras |
Classification： |
18D10, 16T05 |
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