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 corre- spondence between the isomorphisms classes of H-cleft ...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 corre- spondence 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 H2φZ（AH） （H, Z（AH））, where Z（AH） is the center of AH.展开更多
基金supported by the project of Ministerio de Ciencia e Innovación(No.MTM2010-15634)Fondo Europeo de Desarrollo Regional
文摘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 corre- spondence 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 H2φZ（AH） （H, Z（AH））, where Z（AH） is the center of AH.
