对偶拟双代数与预对极的玻色化
Bosonization for dual quasi-bialgebras and preantipode
摘要：
本文将对偶拟双代数（称为玻色化）与$H$上的Yetter-Drinfeld模范畴中的每个对偶拟双代数$H$和每个双代数$R$相关联.然后，利用基本定理，我们刻画了具有投影的对偶拟双代数到具有预对极的对偶拟双代数上的玻色化。作为应用，我们研究了具有对偶Chevalley性质的对偶拟双代数$A$所对应的分次余代数$grA$的结构（例如指出了$A$）.
英文摘要：
In this paper, we associate a dual quasi-bialgebra, called bosonization, to every dual quasi-bialgebra $H$ and every bialgebra $R$ in the category of Yetter-Drinfeld modules over $H$. Then, using the fundamental theorem, we characterize as bosonizations the dual quasi-bialgebras with a projection onto a dual quasi-bialgebra with a preantipode. As an application we investigate the structure of the graded coalgebra $grA$ associated to a dual quasi-bialgebra $A$ with the dual Chevalley property (e.g. $A$ is pointed).
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