@article{Wang2022, 
author = {Shengxiang Wang and Xiaohui Zhang and Shuangjian Guo},
title = {The Hom-Long dimodule category and nonlinear equations},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {1},
pages = {362-381},
keywords = {Yang-Baxter equation, Hom-Long dimodule, Hom-Yetter-Drinfeld category, Hom-Long equation},
url = {https://www.sciopen.com/article/10.3934/era.2022019},
doi = {10.3934/era.2022019},
abstract = {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  HBL is an autonomous category. Second, we prove that the category  HBL 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  HBL can be viewed as a subcategory of the Hom-Yetter-Drinfeld category  H⊗BH⊗BHYD. Finally, we obtain a solution of the Hom-Long equation from the Hom-Long dimodules.}
}