带弱内射的Hopf代数结构  

The Structure of Hopf Algebras with a Weak Injection

作　　者：乐珏[1] 张勇[1] 

机构地区：[1]扬州大学数学科学学院,扬州225002

出　　处：《数学物理学报（A辑）》2005年第2期201-212,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金 (1 0 471 1 2 1 )资助

摘　　要：利用已知Hopf代数构造新的Hopf代数是Hopf代数理论中最基本的问题之一.该文给出了Smash积A#H为Hopf代数,H是A#H的商Hopf代数,且具有弱内射H→A#H的充分必要条件.易证,此种构造推广了Radford和Majid等人所构造的双积和双交叉积等结构.Constructing a new Hopf algebra with known Hopf algebras is one of the most important problems in studying Hopf algebra. In this paper, the authors derive necessary and sufficient conditions for the smash product algebra A#H to be a Hopf algebra with a Hopf quotient algebra H and a weak injection from H to A#H. It is easy to find that this structure includes the Radford’s biproduct and Majid’s bicrossed product as special cases.

关 键 词：HOPF代数 交叉积 SMASH积 弱内射 

分 类 号：O153.3[理学—数学]