论文标题
霍姆长的Dimodule类别和非线性方程
The Hom-Long dimodule category and nonlinear equations
论文作者
论文摘要
在本文中，我们在两个hom-hopf algerbas $（h，α）$和$（b，β）$上构建了一种新的编织单体类别，并将其与两个非线性方程相关联。我们首先介绍$（H，b）$ - hom-hong dimodule的概念，并表明hom-long dimodule类别$^{b} _ {h} \ bbb l $是自主类别。其次，我们证明，如果$（h，α）$是quasitriangular，则类别$^{b} _ {h} \ bbb l $是一个编织的单体类别，而$（b，β）$是共夸氏ianguarl，并获得量子yang-yang-baxter-barbar-barbar-barbar-barbar-barbar-barbare。另外，我们表明类别$^{b} _ {h} \ bbb l $可以看作是hom-yetter-drinfeld类别的子类别$^{høb} _ {høb} _ {høb} \ bbb \ bbb {hyd} $。最后，我们从HOM长的Dimodules获得了Hom长方程的溶液。
In this paper, we construct a kind of new braided monoidal category over two Hom-Hopf algerbas $(H,α)$ and $(B,β)$ and associate it with two nonlinear equations. We first introduce the notion of an $(H,B)$-Hom-Long dimodule and show that the Hom-Long dimodule category $^{B}_{H} \Bbb L$ is an autonomous category. Second, we prove that the category $^{B}_{H} \Bbb L$ is a braided monoidal category if $(H,α)$ is quasitriangular and $(B,β)$ is coquasitriangular and get a solution of the quantum Yang-Baxter equation. Also, we show that the category $^{B}_{H} \Bbb L$ can be viewed as a subcategory of the Hom-Yetter-Drinfeld category $^{HøB}_{HøB} \Bbb {HYD}$. Finally, we obtain a solution of the Hom-Long equation from the Hom-Long dimodules.
