International Journal of Mathematics ( IF 0.604 ) Pub Date : 2020-06-23 , DOI: 10.1142/s0129167x20500585 Dongdong Yan; Shuanhong Wang
Let be a Hom–Hopf T-coalgebra over a group (i.e. a crossed Hom–Hopf -coalgebra). First, we introduce and study the left–right -Yetter–Drinfel’d category over , with , and construct a class of new braided T-categories. Then, we prove that a Yetter–Drinfel’d module category is a full subcategory of the center of the category of representations of . Next, we define the quasi-triangular structure of and show that the representation crossed category is quasi-braided. Finally, the Drinfel’d construction of is constructed, and an equivalent relation between and the representation of is given.