关于辫群重构和辫双的几点注记
Some Remarks on Braided Group Reconstruction and Braided Doubles
摘要：
对于编织范畴$C$中的编织群$B$，由$C^B\to C$通过Tannaka-Krein重构得到交叉余积编织群$Aut(C) \rcocross B$.我们应用这种结构，以获得部分解决方案的两个问题在辫子群理论，即张量问题和辫子双。我们得到了$Aut(C)\rcocross Aut(C)\isom Aut(C)\lcross Aut(C)$和更高的编织群“自旋链”。辫子群$B(R)\lcross B(R)\lcross...\lcross B(R)$的例子明确地描述了R-矩阵关系。我们还得到了$Aut(C)\rcocross Aut(C)^*$作为一个对偶拟三角“codouble”辫子群的重建从对偶范畴$C^\circ\to C$。一般的编织双叉积$B\dcross C$也被考虑。
英文摘要：
The cross coproduct braided group $Aut(C) \rcocross B$ is obtained by Tannaka-Krein reconstruction from $C^B\to C$ for a braided group $B$ in braided category $C$. We apply this construction to obtain partial solutions to two problems in braided group theory, namely the tensor problem and the braided double. We obtain $Aut(C)\rcocross Aut(C)\isom Aut(C)\lcross Aut(C)$ and higher braided group `spin chains'. The example of the braided group $B(R)\lcross B(R)\lcross...\lcross B(R)$ is described explicitly by R-matrix relations. We also obtain $Aut(C)\rcocross Aut(C)^*$ as a dual quasitriangular `codouble' braided group by reconstruction from the dual category $C^\circ\to C$. General braided double crossproducts $B\dcross C$ are also considered.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
