| Title:
|
The bicrossed products of $H_4$ and $H_8$ (English) |
| Author:
|
Lu, Daowei |
| Author:
|
Ning, Yan |
| Author:
|
Wang, Dingguo |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
4 |
| Year:
|
2020 |
| Pages:
|
959-977 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $H_4$ and $H_8$ be the Sweedler's and Kac-Paljutkin Hopf algebras, respectively. We prove that any Hopf algebra which factorizes through $H_8$ and $H_4$ (equivalently, any bicrossed product between the Hopf algebras $H_8$ and $H_4$) must be isomorphic to one of the following four Hopf algebras: $H_8\otimes H_4,H_{32,1},H_{32,2},H_{32,3}$. The set of all matched pairs $(H_8,H_4,\triangleright ,\triangleleft )$ is explicitly described, and then the associated bicrossed product is given by generators and relations. (English) |
| Keyword:
|
Kac-Paljutkin Hopf algebra |
| Keyword:
|
Sweedler's Hopf algebra |
| Keyword:
|
bicrossed product |
| Keyword:
|
factorization problem |
| MSC:
|
16S40 |
| MSC:
|
16T05 |
| MSC:
|
16T10 |
| idZBL:
|
07285973 |
| idMR:
|
MR4181790 |
| DOI:
|
10.21136/CMJ.2020.0079-19 |
| . |
| Date available:
|
2020-11-18T09:43:15Z |
| Last updated:
|
2023-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148405 |
| . |
| Reference:
|
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