Crossed Products over Weak Hopf Algebras Related to Cleft Extensions and Cohomology

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...

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Bibliographic Details
Published in:Chinese annals of mathematics. Serie B 2014-03, Vol.35 (2), p.161-190
Main Author: Jose Nicanor Alonso ALVAREZ Jose Manuel FernAndez VILABOA Ramdn Gonaxlez RODRIGUEZ
Format: Article
Language:English
Subjects:
Applications of Mathematics
H-余模代数
Mathematics
Mathematics and Statistics
上同调群
交叉积
代数结构
弱Hopf代数
等价类
裂缝扩展
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Summary: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.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-014-0828-x