Constructing Quasitriangular Hopf Algebras
Constructing Quasitriangular Hopf Algebras
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DOI：
10.1080/00927872.2013.876036
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发表时间：
2015-01
影响因子：
0.7
通讯作者：
Quan-guo Chen;Ding-Guo Wang
中科院分区：
文献类型：
--
作者：
Quan-guo Chen;Ding-Guo Wang
本文致力于构造拟三角双代数（或Hopf代数）.我们使用的工具是一个新的余积，我们称之为统一余积，在这种结构中，一个Hopf代数和一个代数通过三个代数映射连接：两个余作用和一个广义余圈。双代数余作用于余代数的交叉余积和两个双代数的双交叉余积都是统一余积的特殊情况。然后，我们建立了一个双射对应的所有拟三角结构的集合之间的任意统一的上积和一个特定的一组数据有关的组件的统一的上积。作为主要应用，我们得到了交叉余积（或双交叉余积）是拟三角Hopf代数的充要条件。
This paper is devoted to constructing quasitriangular bialgebras (or Hopf algebras). The tool we use is a new coproduct, we call it the unified coproduct, in the construction of which a Hopf algebra and an algebra are connected by three algebra maps: two coactions and a generalized cocycle. Both the crossed coproduct of a bialgebra coacting on a coalgebra and the bicrossed coproduct of two bialgebras are special cases of the unified coproduct. Then we establish a bijective correspondence between the set of all quasitriangular structures on the arbitrary unified coproduct and a certain set of datum related to the components of the unified coproduct. As the main application, we derive the necessary and sufficient conditions for the crossed coproduct (or bicrossed coproduct) to be a quasitriangular Hopf algebra.