In this paper, we first give the definitions of a crossed left π-H-comodules over a crossed weak Hopf π-algebra H, and show that the category of crossed left π-H-comodules is a monoidal category. Finally, we show t...In this paper, we first give the definitions of a crossed left π-H-comodules over a crossed weak Hopf π-algebra H, and show that the category of crossed left π-H-comodules is a monoidal category. Finally, we show that a family σ = {σα,β： Hα Hβ→ k}α,β∈πof k-linear maps is a coquasitriangular structure of a crossed weak Hopf π-algebra H if and only if the category of crossed left π-H-comodules over H is a braided monoidal category with braiding defined by σ.展开更多
Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to b...Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to be a bialgebra are proved. Then, B#^τδH is a coquasitriangular Hopf algebra under certain conditions. This coquasitriangular Hopf algerbra generalizes some known cross products. Finally, as an application, an explicit example is given.展开更多
In this paper,we show that if H is a finite dimensional Hopf algebra then H is quasitri-angular if and only if H is coquasi-triangular. As a consequentility ,we obtain a generalized result of Sauchenburg.
基金Supported by the Natural Science Foundation of Jiangsu Province(Grant No.BK2012736)the Fund of Science and Technology Department of Guizhou Province(Grant No.2014GZ81365)
文摘In this paper, we first give the definitions of a crossed left π-H-comodules over a crossed weak Hopf π-algebra H, and show that the category of crossed left π-H-comodules is a monoidal category. Finally, we show that a family σ = {σα,β： Hα Hβ→ k}α,β∈πof k-linear maps is a coquasitriangular structure of a crossed weak Hopf π-algebra H if and only if the category of crossed left π-H-comodules over H is a braided monoidal category with braiding defined by σ.
文摘Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to be a bialgebra are proved. Then, B#^τδH is a coquasitriangular Hopf algebra under certain conditions. This coquasitriangular Hopf algerbra generalizes some known cross products. Finally, as an application, an explicit example is given.
基金Partially supported by the National Natural Science Foundation of China.
文摘In this paper,we show that if H is a finite dimensional Hopf algebra then H is quasitri-angular if and only if H is coquasi-triangular. As a consequentility ,we obtain a generalized result of Sauchenburg.
