Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbric...Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.展开更多
In this paper the integrals of entwining structure (A,C,ψ) are discussed, where A is a k-algebra, C a k-coalgebra and a k-linear map. We prove that there exists a normalized integral γ:C→Hom(C,A) of (A,C,ψ) if and...In this paper the integrals of entwining structure (A,C,ψ) are discussed, where A is a k-algebra, C a k-coalgebra and a k-linear map. We prove that there exists a normalized integral γ:C→Hom(C,A) of (A,C,ψ) if and only if any representation of (A,C,ψ) is injective in a functorial way as a corepresentation of C. We give the dual results as well.展开更多
In this paper, we reveal that a weak entwining structure admits a rich cohomology theory. As an application we compute the cohomology of a weak entwining structure associated to a weak coalgebra-Galois extension.
In this paper we obtain a criterion under which the bijectivity of the canonical morphism of a weak Galois extension associated to a weak invertible entwining structure is equivalent to the existence of a strong conne...In this paper we obtain a criterion under which the bijectivity of the canonical morphism of a weak Galois extension associated to a weak invertible entwining structure is equivalent to the existence of a strong connection form. Also we obtain an explicit formula for a strong connection under equivariant projective conditions or under coseparability conditions.展开更多
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
文摘Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.
文摘In this paper the integrals of entwining structure (A,C,ψ) are discussed, where A is a k-algebra, C a k-coalgebra and a k-linear map. We prove that there exists a normalized integral γ:C→Hom(C,A) of (A,C,ψ) if and only if any representation of (A,C,ψ) is injective in a functorial way as a corepresentation of C. We give the dual results as well.
文摘In this paper, we reveal that a weak entwining structure admits a rich cohomology theory. As an application we compute the cohomology of a weak entwining structure associated to a weak coalgebra-Galois extension.
基金Supported by Ministerio de Educació n, Xunta de Galicia and by FEDER (Grant Nos. MTM2010-15634,MTM2009-14464-C02-01, PGIDT07PXB322079PR)
文摘In this paper we obtain a criterion under which the bijectivity of the canonical morphism of a weak Galois extension associated to a weak invertible entwining structure is equivalent to the existence of a strong connection form. Also we obtain an explicit formula for a strong connection under equivariant projective conditions or under coseparability conditions.
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.
