Bicrossed products of generalized Taft algebra and group algebras

Dingguo Wang; Xiangdong Cheng; Daowei Lu

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 3, page 801-816
  • ISSN: 0011-4642

Abstract

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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 ) ⋈ 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 ) ♯ 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 ) ⋈ k [ C n 1 × C n 2 ] is completely presented by generators and relations, where C n denotes the n -cyclic group.

How to cite

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Wang, Dingguo, Cheng, Xiangdong, and Lu, Daowei. "Bicrossed products of generalized Taft algebra and group algebras." Czechoslovak Mathematical Journal 72.3 (2022): 801-816. <http://eudml.org/doc/298349>.

@article{Wang2022,
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.},
author = {Wang, Dingguo, Cheng, Xiangdong, Lu, Daowei},
journal = {Czechoslovak Mathematical Journal},
keywords = {generalized Taft algebra; factorization problem; bicrossed product},
language = {eng},
number = {3},
pages = {801-816},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bicrossed products of generalized Taft algebra and group algebras},
url = {http://eudml.org/doc/298349},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Wang, Dingguo
AU - Cheng, Xiangdong
AU - Lu, Daowei
TI - Bicrossed products of generalized Taft algebra and group algebras
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 3
SP - 801
EP - 816
AB - 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.
LA - eng
KW - generalized Taft algebra; factorization problem; bicrossed product
UR - http://eudml.org/doc/298349
ER -

References

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