交叉积Hopf代数(英文)

Cross Product Hopf Algebras

Drinfelddouble是一种非常重要的拟三角Hopf代数 .SMajid推广了Drinfelddouble ,并且构造了双交叉积A H[1 ,2 ] .王栓宏等构造的双重双交叉积是一种更一般的积[3 ] .双重双交叉积推广了双重交叉 (余 )积、双交叉积、双积、Drinfelddouble和Smash(余 )积 .辫子张量范畴是由AJoyal和RStreet引入的[4] .在它们中的代数结构 ,尤其Hopf代数结构由SMajid引入 .张寿传和陈惠香在辫子张量范畴中构造了双重双交叉积D =Aα ψβH ,并且给出了它成为双代数的充要条件[5] .YBespalove和BDrabant去掉了双重双交叉积的一些条件后 ,在辫子张量范畴中 ,定义了交叉积双代数[6,7] .我们证明了当A和H都有对极时 ,它们构成的双叉积双代数D =Aφ1 ,2 ×φ2 ,1

The Drinfeld double D(H) is a very useful quasi-triangular Hopf algebra. S Majid generalized the Drinfeld double and constructed a double crossproduct A H(1.2). Double bicrossproduct Aα∅ α-ev H, which was constructed by W Zhao, S Wang and Z Jiao[3], is a more generalized product. The double bicrossproduct generalizes double cross products (coproducts), bicrossproducts, biproducts, Drinfeld double, and smash products (coproducts). Braided tensor categories were introduced by A Joyal and R Street[4]. Algebraic structures within them, especially Hopf algebras were introduced by S Majid. The author Shouchuan Zhang and H Chen constructed the double bicrossproduct D = Aζ∅ βΨ H in braided tensor categories and gave the necessary and sufficient conditions for D to be a bialgebra[5]. Y Bespalove and B Drabant stripped off some conditions of double bicrossproduct and defined the cross product bialgebras in braided tensor categories [6.7]. We show that cross product bialgebra D = Aφ1.2 × φ2.1 H is a Hopf algebra when both A and H have antipodes.