Crossed products over weak Hopf algebras related to cleft extensions and cohomology

被引：5

作者：

Alonso Alvarez, Jose Nicanor ^{[1
]}

Fernandez Vilaboa, Jose Manuel ^{[2
]}

Gonzalez Rodriguez, Ramon ^{[3
]}

机构：

[1] Univ Vigo, Dept Matemat, E-36280 Vigo, Spain

[2] Univ Santiago de Compostela, Dept Alxebra, E-15771 Santiago De Compostela, Spain

[3] Univ Vigo, Dept Matemat Aplicada 2, E-36310 Vigo, Spain

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2014年 / 35卷 / 02期

关键词：

Monoidal category; Weak Hopf algebra; Cleft extension; Weak crossed product; Sweedler cohomology for weak Hopf algebras; GALOIS EXTENSIONS; MONADS;

D O I：

10.1007/s11401-014-0828-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 A (H) a dagger(a) A, where A (H) is the subalgebra of coinvariants, and the equivalence classes of crossed systems for H over A (H) . 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 (H,Z(A (H) )), where Z(A (H) ) is the center of A (H) .

引用

页码：161 / 190

页数：30

共 23 条

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