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Hopf-Galois extensions for monoidal Hom-Hopf algebras

100%
Chen Y., Zhang L.
Colloquium Mathematicum
|
2016
|
tom 143
|
nr 1
127-147
EN
Hopf-Galois extensions for monoidal Hom-Hopf algebras are investigated. As the main result, Schneider's affineness theorem in the case of monoidal Hom-Hopf algebras is shown in terms of total integrals and Hopf-Galois extensions. In addition, we obtain an affineness criterion for relative Hom-Hopf modules which is associated with faithfully flat Hopf-Galois extensions of monoidal Hom-Hopf algebras.
2
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Separable and Frobenius monoidal Hom-algebras

100%
Chen Y., Zhou X.
Colloquium Mathematicum
|
2014
|
tom 137
|
nr 2
229-251
EN
As generalizations of separable and Frobenius algebras, separable and Frobenius monoidal Hom-algebras are introduced. They are all related to the Hom-Frobenius-separability equation (HFS-equation). We characterize these two Hom-algebraic structures by the same central element and different normalizing conditions, and the structure of these two types of monoidal Hom-algebras is studied. The Nakayama automorphisms of Frobenius monoidal Hom-algebras are considered.
3
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The fundamental theorem and Maschke's theorem in the category of relative Hom-Hopf modules

81%
Chen Y., Wang Z., Zhang L.
Colloquium Mathematicum
|
2016
|
tom 144
|
nr 1
55-71
EN
We introduce the concept of relative Hom-Hopf modules and investigate their structure in a monoidal category $𝓗̃ (ℳ_{k})$. More particularly, the fundamental theorem for relative Hom-Hopf modules is proved under the assumption that the Hom-comodule algebra is cleft. Moreover, Maschke's theorem for relative Hom-Hopf modules is established when there is a multiplicative total Hom-integral.
4
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Quasitriangular Hom-Hopf algebras

81%
Chen Y., Wang Z., Zhang L.
Colloquium Mathematicum
|
2014
|
tom 137
|
nr 1
67-88
EN
A twisted generalization of quasitriangular Hopf algebras called quasitriangular Hom-Hopf algebras is introduced. We characterize these algebras in terms of certain morphisms. We also give their equivalent description via a braided monoidal category $𝓗̃ (_Hℳ )$. Finally, we study the twisting structure of quasitriangular Hom-Hopf algebras by conjugation with Hom-2-cocycles.
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