| Title:
|
Quasitriangular Hopf group algebras and braided monoidal categories (English) |
| Author:
|
Zhao, Shiyin |
| Author:
|
Wang, Jing |
| Author:
|
Chen, Hui-Xiang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
893-909 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Hopf $\pi $-algebra |
| Keyword:
|
$H$-$\pi $-modules |
| Keyword:
|
braided monoidal category |
| Keyword:
|
braided monoidal functor |
| MSC:
|
08C05 |
| MSC:
|
16T05 |
| MSC:
|
16T25 |
| MSC:
|
18D10 |
| idZBL:
|
Zbl 06433703 |
| idMR:
|
MR3304787 |
| DOI:
|
10.1007/s10587-014-0142-5 |
| . |
| Date available:
|
2015-02-09T17:23:58Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144150 |
| . |
| Reference:
|
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| Reference:
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| . |
