New Braided Crossed Categories and Drinfel'd Quantum Double for Weak Hopf Group Coalgebras
New Braided Crossed Categories and Drinfel'd Quantum Double for Weak Hopf Group Coalgebras
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DOI：
10.1080/00927870701509420
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发表时间：
2008-05
影响因子：
0.7
通讯作者：
A. V. Daele;Shuanhong Wang
中科院分区：
文献类型：
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作者：
A. V. Daele;Shuanhong Wang
为了构造一类新的Turaev意义下的辫状交叉范畴（cf. Turaev，1994，2000），首先研究了货车Daele和Wang（2004）中引入的弱Hopf群余代数的一些性质.然后，我们推广了Böhm等（1999）和Virelizier（2002）中的弱Hopf群余模的基本定理，以及弱交叉结构上的Yetter-Drinfel'd模的概念，推广Böhm（2000）和Zunino（2004 a）的结果通过使用Caenepeel和De Lombaerde（2006）在他们的文章中介绍的Turaev范畴理论的方法。最后，在弱交叉Hopf群余代数上，我们引入了Drinfel'd量子double结构的一个类似物，并证明了这种Drinfel'd量子double上的模范畴同构于Yetter-Drinfel'd模范畴作为一类新的辫子交叉范畴.
In order to construct a class of new braided crossed categories in the sense of Turaev (cf. Turaev, 1994, 2000), we first study some properties of a weak Hopf group-coalgebra introduced in Van Daele and Wang (2004). Then, we develop the fundamental theorem of weak Hopf group-comodules, generalizing the ones both in Böhm et al. (1999) and in Virelizier (2002), and the concept of Yetter–Drinfel'd module over weak crossed structures, generalizing the ones both in Böhm (2000) and Zunino (2004a) by using an approach of Turaev categorical theory introduced in their article by Caenepeel and De Lombaerde (2006). Finally, over a weak crossed Hopf group-coalgebra we introduce an analog of a Drinfel'd quantum double construction and show that the category of modules over the such Drinfel'd quantum doubles is isomorphic to the category of Yetter–Drinfel'd modules as a class of new braided crossed categories.