Hom-Long双模范畴与非线性方程
The Hom-Long dimodule category and nonlinear equations
摘要：
本文在两个Hom-Hopf代数$(H,α)$和$(B,β)$上构造了一类新的辫幺幺半范畴，并将其与两个非线性方程联系起来.首先引入$(H,B)$ -Long双模的概念，证明了Hom-Long双模范畴$^{B}_{H} \Bbb L$是一个自治范畴.其次，证明了范畴$^{B}_{H} \Bbb L$是辫子幺半范畴，如果$(H,α)$是拟三角的，$(B,β)$是余拟三角的，并得到了量子杨-巴克斯特方程的一个解。此外，我们证明了范畴$^{B}_{H} \Bbb L$可以被看作是Hom-Yetter-Drinfeld范畴$^{HøB}_{HøB} \Bbb {HYD}$的一个子类。最后，我们利用Hom-Long双模得到了Hom-Long方程的一个解.
英文摘要：
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.
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