The Hom-Long dimodule category and nonlinear equations.

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 H B L is an autonomous category. Second, we prove that the category H B 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 H B L can be viewed as a subcategory of the Hom-Yetter-Drinfeld category H ⊗ B H ⊗ B H Y D . Finally, we obtain a solution of the Hom-Long equation from the Hom-Long dimodules. [ABSTRACT FROM AUTHOR]