群Yetter-Drinfel'd范畴中的Hopf代数

Hopf Algebras in Group Yetter-Drinfel'd Categories

中文关键词:  交叉Hopf群余代数  群余模似对象  群(余)模(余)代数.

英文关键词:Crossed Hopf group-coalgebra  group-comodulelike object  group-(co)module (co)algebra.

中文摘要:

      在此文中我们首先证明如果$H$是基于交叉Hopf群余代数上的群Yetter-Drinfel'd范畴$^{L}_{L}\mathcal {YD}(\pi)$ 中的一个有限维Hopf代数, 那么它的对偶 $H^*$也是此中的Hopf代数. 然后我们建立此范畴中的$H$-Hopf模基本定理.

英文摘要:

      In this note we first show that if $H$ is a finite-dimensional Hopf algebra in a group Yetter-Drinfel'd category $^{L} _{L}{\mathcal {YD}}(\pi)$ over a crossed Hopf group-coalgebra $L$, then its dual $H^*$ is also a Hopf algebra in the category $^{L} _{L}{\mathcal {YD}}(\pi) $. Then we establish the fundamental theorem of Hopf modules for $H$ in the category $^{L} _{L}{\mathcal {YD}}(\pi)$.