Quasitriangular Hopf group algebras and braided monoidal categories

Zhao, Shiyin, Wang, Jing, and Chen, Hui-Xiang. "Quasitriangular Hopf group algebras and braided monoidal categories." Czechoslovak Mathematical Journal 64.4 (2014): 893-909. <http://eudml.org/doc/269848>.

@article{Zhao2014,
abstract = {Let $\pi $ be a group, and $H$ be a semi-Hopf $\pi $-algebra. We first show that the category $_H\{\mathcal \{M\}\}$ of left $\pi $-modules over $H$ is a monoidal category with a suitably defined tensor product and each element $\alpha $ in $\pi $ induces a strict monoidal functor $F_\{\alpha \}$ from $_H\{\mathcal \{M\}\}$ to itself. Then we introduce the concept of quasitriangular semi-Hopf $\pi $-algebra, and show that a semi-Hopf $\pi $-algebra $H$ is quasitriangular if and only if the category $_H\mathcal \{M\}$ is a braided monoidal category and $F_\{\alpha \}$ is a strict braided monoidal functor for any $\alpha \in \pi $. Finally, we give two examples of Hopf $\pi $-algebras and describe the categories of modules over them.},
author = {Zhao, Shiyin, Wang, Jing, Chen, Hui-Xiang},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hopf $\pi $-algebra; $H$-$\pi $-modules; braided monoidal category; braided monoidal functor; semi-Hopf $\pi $-algebras; -modules; quasitriangular semi-Hopf algebras; braided monoidal categories; braided monoidal functors; tensor products; coalgebras},
language = {eng},
number = {4},
pages = {893-909},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Quasitriangular Hopf group algebras and braided monoidal categories},
url = {http://eudml.org/doc/269848},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Zhao, Shiyin
AU - Wang, Jing
AU - Chen, Hui-Xiang
TI - Quasitriangular Hopf group algebras and braided monoidal categories
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 893
EP - 909
AB - Let $\pi $ be a group, and $H$ be a semi-Hopf $\pi $-algebra. We first show that the category $_H{\mathcal {M}}$ of left $\pi $-modules over $H$ is a monoidal category with a suitably defined tensor product and each element $\alpha $ in $\pi $ induces a strict monoidal functor $F_{\alpha }$ from $_H{\mathcal {M}}$ to itself. Then we introduce the concept of quasitriangular semi-Hopf $\pi $-algebra, and show that a semi-Hopf $\pi $-algebra $H$ is quasitriangular if and only if the category $_H\mathcal {M}$ is a braided monoidal category and $F_{\alpha }$ is a strict braided monoidal functor for any $\alpha \in \pi $. Finally, we give two examples of Hopf $\pi $-algebras and describe the categories of modules over them.
LA - eng
KW - Hopf $\pi $-algebra; $H$-$\pi $-modules; braided monoidal category; braided monoidal functor; semi-Hopf $\pi $-algebras; -modules; quasitriangular semi-Hopf algebras; braided monoidal categories; braided monoidal functors; tensor products; coalgebras
UR - http://eudml.org/doc/269848
ER -