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Then, some regular semigroups were constructed by using of weak antipodes of some weak Hopf algebras. 然后用某些弱 Hopf代数的弱对极构造正则半群 .
In this paper,(A,SA) and(H,SH) both are weak Hopf algebras on a field k. A is also an H-module algebra. (A,SA)和(H,SH)都是数域k上的弱Hopf代数,并且A是右H-余模代数。
Last, the role of weak antipodes in the structures of modules/ comodules over a weak Hopf algebra is presented. 最后给出的一些结果体现了弱对极在弱 Hopf代数上的模 /余模结构中的作用 .
It generalizes the theories of Yetter-Drinfeld modules on Hopf algebras, and associates the weak Doi-Hopf modules , quantum Yetter-Drinfeld modules with relative weak Hopf modules. 它推广了Hopf代数上Yetter-Drinfeld模的一些理论,并给出了弱Doi-Hopf模,量子Yetter-Drinfeld模与相关弱Hopf模三者之间的关系。
A well-known example is weak Hopf algebra, which is introduced in [L2] for studying the non-invertible solution of Yang-Baxter Equation based on this class of bialgebras (in [L2] and [L6]). 在文献[L2]中，为了研究Yang-Baxter方程的非平凡解，作者引入了著名的弱Hopf代数的概念使得基于这一类双代数，能够给出Yang-Baxter方程的一个非平凡解。
semiquasitriangular weak Hopf algebra 半拟三角弱Hopf代数
Integrality of Module Algebras over its Invariant over Weak Hopf Algebra 弱Hopf代数的模代数在其不变量上的积分
weak Hopf algebras 弱Hopf代数
weak Hopf algebra 弱Hopf代数
In this paper,we prove that if H is a cocomutative finite dimensional weak Hopf alegbra and A is a commutative H-module algebra,A is integral over its invariant AH. 主要研究关于弱Hopf代数的模代数在其不变量上的积分;设H是余可换的有限维的弱Hopf代数;A是可换的左H-模代数;那么A是其不变量AH上的积分.
Let L and A be Hopf algebras on field k with antipodes SL and SA,and let C be a right A-module coalgebra. 设L是域k上的Hopf代数,其对极为SL;
Modern algebras, Homological algebras, Representation theory of algebras, Lie algebras, Hopf algebras. 教课领域：近世代数, 同调代数, 代数表示, 李代数，Hopf代数；
weak quasitriangle Hopf algebras 弱拟三角Hoof代数
NI Shen-bing.Weak Hopf algebras's twisted Smash product and Smach coproduct [J].J of Zhejiang University (Science Edition), 2002, 29(3): 268-273. [8]倪沈冰.;弱Hopf代数的扭曲的Smash积及Smash余积[J]
In addition, if B=H is a Hopf algebra with antipodes, then H0 is a Hopf algebra with antipodes S . 而且，如果B=H是一个带有对极S的Hopf代数，那么H~0是一个带有对极S~*的Hopf代数。
Some basic conclusions and their improper proofs in "Hopf Algebra"(E.Abe) are amended and improved in this paper. 本文对专著“Hopf Algebra”(E.;Abe)中若干基本结论或其证明的不妥或错误之处进行了修正和改进
In the second part of this thesis we prove that if the Hopf Galois extension is cocentral, and the invariants is a Hopf algebra then $A$ is itself a Hopf algebra. 设%24H%24是域%24k%24上的余半单Hopf代数，%24A%24为双代数且%24H%24在%24A%24上有余作用，在论文的第二部分我们证明了当%24A%24是其余不变量的Galois余中心扩张时，%24A%24上有Hopf代数结构当且仅当它的余不变量子双代数是 Hopf代数。
Then in [2], [3], [4] and [5], the authors have discussed the structures of twisted Hopf algebras and bitwisted Hopf algebras and studied some properties of their antipodes, and so on. 在文献[2]、[3]、[4]和[5]中;作者分别研究了扭Hopf代数和双扭Hopf代数的结构和反极元的性质等.;本文主要研究双扭Hopf代数的对偶空间;以及两个双扭Hopf代数的对偶关系
Let L and A be Hopf algebras on field k with antipodes s_L and s_A, B being a right A-comodule algebra, C a right A-module coalgebra. The defination of (A, B)-Hopf module and the fundamental structure theorem on (A, B)-Hopf module in L_LYD were given. 设L是域k上的Hopf代数;其对极为sL; A是-Hopf代数;其对极为sA;B是右A余模代数;C是右A模余代数;给出LLYD中(A;B)Hopf模的定义以及LLYD中(A;B)-Hopf模的基本结构定理;并讨论了其对偶情况.
The spirit is willing but the flesh is weak. 心有余而力不足。