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Volume 30, Issue 4
A Note on Generalized Long Modules

Shuangjian Guo & Lihong Dong

DOI: 10.13447/j.1674-5647.2014.04.05

Commun. Math. Res., 30 (2014), pp. 320-328.

Published online: 2021-05

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  • Abstract

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 $B$.

  • Keywords

Turaev braided group category, generalized Long module, Turaev group-(co)algebra, (co)quasitriangular structure.

  • AMS Subject Headings

16W30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-30-320, author = {Guo , Shuangjian and Dong , Lihong}, title = {A Note on Generalized Long Modules}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {30}, number = {4}, pages = {320--328}, abstract = {

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} }
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 -

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 $B$.

Guo , Shuangjian and Dong , Lihong. (2021). A Note on Generalized Long Modules. Communications in Mathematical Research . 30 (4). 320-328. doi:10.13447/j.1674-5647.2014.04.05
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