CAJ | 학술논문

Drinfeld double 是一种非常重要的拟三角Hopf代数.S Majid推广了Drinfeld double,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、Drinfeld double和Smash(余)积.辫子张量范畴是由A Joyal和R Street引入的[4].在它们中的代数结构,尤其Hopf代数结构由S Majid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αψβH,并且给出了它成为双代数的充要条件[5].Y Bespalove和B Drabant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×φ2,1H是一个Hopf代数.
Drinfeld double 시일충비상중요적의삼각Hopf대수.S Majid추엄료Drinfeld double,병차구조료쌍교차적A H[1,2].왕전굉등구조적쌍중쌍교차적시일충경일반적적[3].쌍중쌍교차적추엄료쌍중교차(여)적、쌍교차적、쌍적、Drinfeld double화Smash(여)적.변자장량범주시유A Joyal화R Street인입적[4].재타문중적대수결구,우기Hopf대수결구유S Majid인입.장수전화진혜향재변자장량범주중구조료쌍중쌍교차적D=AαψβH,병차급출료타성위쌍대수적충요조건[5].Y Bespalove화B Drabant거도료쌍중쌍교차적적일사조건후,재변자장량범주중,정의료교차적쌍대수[6,7].아문증명료당A화H도유대겁시,타문구성적쌍차적쌍대수D=Aφ1,2×φ2,1H시일개Hopf대수.
The Drinfeld double D(H) is a very useful quasi-triagular Hopf algebra.S Majid generalized the Drinfeld double and constructed a double 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].Algbraic structures within them,especially Hopf algebras were introduced by S Majid.The author Shouchuan Zhang and H Chen constructed 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.