BICOVARIANT DIFFERENTIAL CALCULI ON A WEAK HOPF ALGEBRA
BICOVARIANT DIFFERENTIAL CALCULI ON A WEAK HOPF ALGEBRA
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DOI：
10.11650/tjm.18.2014.4046
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发表时间：
2014-11
影响因子：
0.4
通讯作者：
Hai-xing Zhu;Shuanhong Wang;Ju-zhen Chen
中科院分区：
文献类型：
--
作者：
Hai-xing Zhu;Shuanhong Wang;Ju-zhen Chen
设H是具有双射对极的弱Hopf代数。在本文中，我们遵循Woronowicz的基本方法来表征双共变微分演算$H$。我们证明了双共变微分演算与包含在$ ker \vareps_s $中的$H$的某些右理想之间存在1-1对应，使得这些理想是具有余伴随映射的右$H$-余模，其中$\vareps_s$是$H$的源映射.这是著名的量子群上双协变微分演算的Woronowicz定理的推广。
Let $H$ be a weak Hopf algebra with bijective antipode. In this paper we follow Woronowicz's fundamental method to characterize bicovariant differential calculi on $H$. We show that there exists a 1-1 correspondence between bicovariant differential calculi and some right ideals of $H$ contained in $ ker \varepsilon_s $ such that these ideals are right $H$-comodules with coadjoint maps, where $\varepsilon_s$ is the source map of $H$. This is a generalization of well-known Woronowicz's theorem about bicovariant differential calculi on quantum groups.