Let （H, α） be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules H^H HYD is isomorphic t...Let （H, α） be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules H^H HYD is isomorphic to the center of the category of left （H, α）-Hom-modules. Also, by the center construction, we get that the categories of left-left, left-right, right-left, and right-right Hom-Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Second, we prove that the category of finitely generated projective left-left Hom-Yetter-Drinfeld modules has left and right duality.展开更多
It is known that any strict tensor category (C?I) determines a braided tensor categoryZ(C), the centre ofC. WhenA is a finite dimension Hopf algebra, Drinfel’d has proved thatZ(A M) is equivalent to D(A) M as a braid...It is known that any strict tensor category (C?I) determines a braided tensor categoryZ(C), the centre ofC. WhenA is a finite dimension Hopf algebra, Drinfel’d has proved thatZ(A M) is equivalent to D(A) M as a braided tensor category, whereA M is the left A-module category andD(A) is the Drinfel’d double ofA. For a braided tensor category, the braidC U,v is a natural isomorphism for any pair of object (U,V) in. If weakening the natural isomorphism of the braidC U,V to a natural transformation, thenC U,V is a prebraid and the category with a prebraid is called a prebraided tensor category. Similarly it can be proved that any strict tensor category determines a prebraided tensor category Z～ (C), the near centre of. An interesting prebraided tensor structure of the Yetter-Drinfel’d category C*A YD C*A given, whereC # A is the smash product bialgebra ofC andA. And it is proved that the near centre of Doi-Hopf module A M(H) C is equivalent to the Yetter-Drinfel’ d C*A YD C*A as prebraided tensor categories. As corollaries, the prebraided tensor structures of the Yetter-Drinfel’d category A YD A , the centres of module category and comodule category are given.展开更多
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education (20060286006)the FNS of CHINA(10571026)the Southeast University Fund(XJ0707273)
基金Acknowledgements The authors sincerely thank the referees for their valuable suggestions and comments on this paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11601486, 61272007. 11401534）.
文摘Let （H, α） be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules H^H HYD is isomorphic to the center of the category of left （H, α）-Hom-modules. Also, by the center construction, we get that the categories of left-left, left-right, right-left, and right-right Hom-Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Second, we prove that the category of finitely generated projective left-left Hom-Yetter-Drinfeld modules has left and right duality.
文摘It is known that any strict tensor category (C?I) determines a braided tensor categoryZ(C), the centre ofC. WhenA is a finite dimension Hopf algebra, Drinfel’d has proved thatZ(A M) is equivalent to D(A) M as a braided tensor category, whereA M is the left A-module category andD(A) is the Drinfel’d double ofA. For a braided tensor category, the braidC U,v is a natural isomorphism for any pair of object (U,V) in. If weakening the natural isomorphism of the braidC U,V to a natural transformation, thenC U,V is a prebraid and the category with a prebraid is called a prebraided tensor category. Similarly it can be proved that any strict tensor category determines a prebraided tensor category Z～ (C), the near centre of. An interesting prebraided tensor structure of the Yetter-Drinfel’d category C*A YD C*A given, whereC # A is the smash product bialgebra ofC andA. And it is proved that the near centre of Doi-Hopf module A M(H) C is equivalent to the Yetter-Drinfel’ d C*A YD C*A as prebraided tensor categories. As corollaries, the prebraided tensor structures of the Yetter-Drinfel’d category A YD A , the centres of module category and comodule category are given.
基金Supported by NSFC(No.11101288)the Natural Science Foundation of Zhejiang Province(No. Y6110323,No.Y12A010035)+2 种基金Jiangsu Planned Projects for Postdoctoral Research Funds(No.0902081C)Zhejiang Provincial Education Department Project(No.Y200907995)Project of Shaoxing University(No. 09LG1001)
