偶交叉双积Hopf代数B_T_RH的构造  

The Structure of Double Crossed Bi-Product Hopf Algebra B_T ■_R H

作　　者：赵文正[1] 

机构地区：[1]河南师范大学数学系,河南新乡453002

出　　处：《数学学报（中文版）》2000年第4期677-684,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金!19601015;河南省教委资助

摘　　要：本文给出了DoiY．构造的偶交叉积BT■H的代数结构与ReshetikhimN．构造的双代数B■RH的余代数结构在张量空间B■H上构成双代数（记为Bτ■RH）的充要条件，利用此结论具体构造了一个有趣的例子B4■KZ2；证明了当B，H均为Hopf．代数时Bτ■RH也为Hopf代数，最后给出这类双代数的映射刻划。The double crossed-product Bτ■bH by Doi Y. constructed and bialgebra B■bH by Reshetikhim N. constructed are well known in [1, 3], in this paper we find necessary and sufficient conditions for the Bτ■H algebra structure and B■RH coalgebra structure on B■H to afford B■H a bialgebra structure (Let Bτ■H denote the resulting bialgebra). By use this result, we construct an intersting example B4τ■R KZ2. In the final we give characterization of Bτ■R H by introducing the mapping system.

关 键 词：HOPF代数 偶交叉积 偶交叉双积 代数结构 

分 类 号：O153.3[理学—数学]