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Bicrossed products of generalized Taft algebra and group algebras
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 801-816
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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.
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.
DOI : 10.21136/CMJ.2022.0176-21
Classification : 16S40, 16T05
Keywords: generalized Taft algebra; factorization problem; bicrossed product 
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Wang, Dingguo; Cheng, Xiangdong; Lu, Daowei. Bicrossed products of generalized Taft algebra and group algebras. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 801-816. doi: 10.21136/CMJ.2022.0176-21

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