Hopf Algebras in Group Yetter-Drinfel＇d Categories  

作　　者：SHEN Bing Liang WANG Shuan Hong 

机构地区：[1]Department of Mathematics, Southeast University, Jiangsu 210096, China

出　　处：《Journal of Mathematical Research and Exposition》2009年第2期266-274,共9页数学研究与评论（英文版）

基　　金：the Specialized Research Fund for the Doctoral Program of Higher Education （No. 20060286006）; the National Natural Science Foundation of China （No. 10571026）.

摘　　要：In this note we first show that if H is a finite-dimensional Hopf algebra in a group Yetter-Drinfel＇d category L^LyD（π） over a crossed Hopf group-coalgebra L, then its dual H^＊ is also a Hopf algebra in the category L^LyD（π）. Then we establish the fundamental theorem of Hopf modules for H in the category L^LyD（π）.In this note we first show that if H is a finite-dimensional Hopf algebra in a group Yetter-Drinfel＇d category L^LyD（π） over a crossed Hopf group-coalgebra L, then its dual H^＊ is also a Hopf algebra in the category L^LyD（π）. Then we establish the fundamental theorem of Hopf modules for H in the category L^LyD（π）.

关 键 词：Crossed Hopf group-coalgebra group-comodulelike object group- （co） module （co） algebra. 

分 类 号：O153.3[理学—数学]