The question of how the category of entwined modules can be made into a braided monoidal category is studied. First, the sufficient and necessary conditions making the category into a monoidal category are obtained by...The question of how the category of entwined modules can be made into a braided monoidal category is studied. First, the sufficient and necessary conditions making the category into a monoidal category are obtained by using the fact that if （A, C, ψ） is an entwining structure, then A × C can be made into an entwined module. The conditions are that the algebra and coalgebra in question are both bialgebras with some extra compatibility relations. Then given a monodial category of entwined modules, the braiding is constructed by means of a twisted convolution invertible map Q, and the conditions making the category form into a braided monoidal category are obtained similarly. Finally, the construction is applied to the category of Doi-Hopf modules and （α, β ）-Yetter-Drinfeld modules as examples.展开更多
We obtain necessary and sufficient conditions for the functor F ： ∪/Ac （ψ） → Mc on the category of partial entwined modules that forgets the A-action to be separable. As an application, we prove a Maschke-type t...We obtain necessary and sufficient conditions for the functor F ： ∪/Ac （ψ） → Mc on the category of partial entwined modules that forgets the A-action to be separable. As an application, we prove a Maschke-type theorem for the category of partial entwined modules.展开更多
基金Specialized Research Fund for the Doctoral Program of Higher Education(No.20060286006)the National Natural Science Founda-tion of China(No.10571026)
文摘The question of how the category of entwined modules can be made into a braided monoidal category is studied. First, the sufficient and necessary conditions making the category into a monoidal category are obtained by using the fact that if （A, C, ψ） is an entwining structure, then A × C can be made into an entwined module. The conditions are that the algebra and coalgebra in question are both bialgebras with some extra compatibility relations. Then given a monodial category of entwined modules, the braiding is constructed by means of a twisted convolution invertible map Q, and the conditions making the category form into a braided monoidal category are obtained similarly. Finally, the construction is applied to the category of Doi-Hopf modules and （α, β ）-Yetter-Drinfeld modules as examples.
基金The work is supported by the Key University Science Research Project of Anhui Province （KJ2015A294）, the China Postdoctoral Science Foundation （2015M571725）, the Fund of Science and Technology Department of Guizhou Province （2014GZ81365） and the Program for Science and Technology Innovation Talents in Education Department of Guizhou Province （KY[20151481）.
文摘We obtain necessary and sufficient conditions for the functor F ： ∪/Ac （ψ） → Mc on the category of partial entwined modules that forgets the A-action to be separable. As an application, we prove a Maschke-type theorem for the category of partial entwined modules.
