Czechoslovak Mathematical Journal, Vol. 72, No. 3, pp. 801-816, 2022
Bicrossed products of generalized Taft algebra and group algebras
Dingguo Wang, Xiangdong Cheng, Daowei Lu
Received May 6, 2021. Published online February 15, 2022.
Abstract: 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.
Affiliations: Dingguo Wang (corresponding author), School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, P. R. China, e-mail: dgwang@qfnu.edu.cn; Xiangdong Cheng, School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, P. R. China and College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211106, P. R. China; Daowei Lu, Department of Mathematics, Jining University, Qufu, Shandong 273155, P. R. China
