Twisting products of Hopf algebras and quantum double  

作　　者：HU GuoquanDepartment of Mathematics, Zhongshan University, Guangzhou 510275, China 

出　　处：《Chinese Science Bulletin》1999年第4期309-312,共4页

摘　　要：Let σ be a skew pairing on the pair (B, H) of Hopf algebras, and A a left(B, H) bicomodule algebra. A new algebra A_σ, called the twisting product of A, is obtained by alternating the multiplication of A using σ and the coactions on A by B and H. σ induces a skew pairing on (B B,H H), and the regular comodule structures of B and H induce a left (B B,H H) bicomodule algebra structure on B H, and the associated twisting product (B H)is a Hopf algebra, with the tensor coalgebra structure; moreover, A_σ remains a left (B H),comodule algebra. In particular,a description of the Drinfeld double is obtained from the twisting point of view. In addition, smash products appear as special cases. Dually, the construction of twisting coproducts is introduced by using copairings, and the Drinfeld quantum codouble and some smash coproducts are described.Let σ be a skew pairing on the pair (B,H) of Hopf algebras, and A a left (B, H) bicomodule algebra. A new algebraA σ , called the twisting product ofA, is obtained by alternating the multiplication ofA using σ and the coactions onA byB andH. σ induces a skew pairing on (B?B ccp,H?H cp), and the regular comodule structures ofB andH induce a left (B?Bccp, H?Hcp) bicomodule algebra structure onH?H, and the associated twisting product (B?H)σ- is a Hopf algebra, with the tensor coalgebra structure; moreover,A σ remains a left (B?H)σ- comodule algebra. In particular, a description of the Drinfeld double is obtained from the twisting point of view. In addition, smash products appear as special cases. Dually, the construction of twisting coproducts is introduced by using copairings, and the Drinfeld quantum codouble and some smash coproducts are described.

关 键 词：SKEW (co)pairing TWISTING (co)products (co)quantum double. 

分 类 号：O152.5[理学—数学]