TY - JOUR
T1 - A Note on Generalized Long Modules
AU - Guo , Shuangjian
AU - Dong , Lihong
JO - Communications in Mathematical Research 
VL - 4
SP - 320
EP - 328
PY - 2021
DA - 2021/05
SN - 30
DO - http://doi.org/10.13447/j.1674-5647.2014.04.05
UR - https://global-sci.org/intro/article_detail/cmr/18956.html
KW - Turaev braided group category, generalized Long module, Turaev
group-(co)algebra, (co)quasitriangular structure.
AB - <p style="text-align: justify;">Let $_H\mathcal{L}^B$ be the category of generalized Long modules, that is, $H$-modules
and $B$-comodules over Hopf algebras $B$ and $H$. We describe a new Turaev braided
group category over generalized Long module $_H\mathcal{L}^B(\mathcal{F} (π))$ where the opposite group $\mathcal{F} (π)$ of the semidirect product of the opposite group $π^{op}$ of a group $π$ by $π$. As an
application, we show that this is a Turaev braided group-category $_H\mathcal{L}^B$ for a quasitriangular Turaev group-coalgebra $H$ and a coquasitriangular Turaev group-algebra $B$.</p>