Article
| 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 |
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| Category: | math |
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| 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 |
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| Date available: | 2022-08-22T08:23:40Z |
| Last updated: | 2022-12-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/150618 |
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