Commun. Math. Res., 30 (2014), pp. 320-328.
Published online: 2021-05
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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 $B$.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2014.04.05}, url = {http://global-sci.org/intro/article_detail/cmr/18956.html} }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 $B$.