%0 Journal Article
%T Weak Skew Paired Bialgebras and Weak Relative Long Bialgebras<br>弱斜配对双代数和弱相关Long双代数
%A Zhang Liangyun
%A <br>张良云
%J 数学物理学报(A辑)
%D 2006
%I 
%X This paper gives a sufficient andnecessary condition for given twisted product$(H^\sigma,\cdot_\sigma)$ to be a weak bialgebra. If $B, H,\tau]$ are weak skew paired bialgebras and $\tau$ is invertible,then, under some condition, the weakbicrossed product $B\bowtie_\tau H$ is a weak bialgebra. If $(B,H, \sigma)$ is a weak relative Long bialgebra and $\sigma$invertible, then the weak bicrossed product $B^{OP}\bowtie_\sigmaH$ can be constructed. Espically, for the Sweedler 4-dimensionalHopf algebra $H_4$, the author gives an example to show that$(B^{OP}\bowtie_\sigma H_4, \beta)$ is not only a Long bialgebrabut also a non-commutative and non-cocommutative 8-dimensionalHopf algebra, where $B$ is a sub-Hopf algebra of $H_4$. If $B$ and$H$ are weak bialgebras, and $\sigma: B\otimes H\rightarrow k$ isa linear map, then a sufficient and necessary conditionfor $(B,\sigma,\leftharpoonup, \Delta_B)$ to be a weak rightrelative $(H, B)$-dimodule algebra is given.
%K Weak skew paired bialgebra
%K Weak bicrossed product
%K Weak relative long bialgebra
%K Weak relative dimodule algebra<br>弱Doi双代数
%K 弱双交叉积
%K 弱相关Long双代数
%K 弱相关重模代数
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=207FAD39029AACD4&yid=37904DC365DD7266&vid=96C778EE049EE47D&iid=E158A972A605785F&sid=ED9DF3402785F68D&eid=FED67FBA0A707330&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=15