| Title:
|
Bicrossed products of generalized Taft algebra and group algebras (English) |
| Author:
|
Wang, Dingguo |
| Author:
|
Cheng, Xiangdong |
| Author:
|
Lu, Daowei |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
801-816 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a group generated by a set of finite order elements. We prove that any bicrossed product $H_{m,d}(q)\bowtie k[G]$ between the generalized Taft algebra $H_{m,d}(q)$ and group algebra $k[G]$ is actually the smash product $H_{m,d}(q)\sharp k[G]$. Then we show that the classification of these smash products could be reduced to the description of the group automorphisms of $G$. As an application, the classification of $H_{m,d}(q)\bowtie k[ C_{n_1}\times C_{n_2}]$ is completely presented by generators and relations, where $C_n$ denotes the $n$-cyclic group. (English) |
| Keyword:
|
generalized Taft algebra |
| Keyword:
|
factorization problem |
| Keyword:
|
bicrossed product |
| MSC:
|
16S40 |
| MSC:
|
16T05 |
| idZBL:
|
Zbl 07584103 |
| idMR:
|
MR4467943 |
| DOI:
|
10.21136/CMJ.2022.0176-21 |
| . |
| Date available:
|
2022-08-22T08:23:40Z |
| Last updated:
|
2024-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150618 |
| . |
| Reference:
|
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