{"title":"PBW-deformations of smash products involving Hopf algebra of Kac-Paljutkin type","authors":"Yujie Gao, Shilin Yang","doi":"arxiv-2408.16557","DOIUrl":null,"url":null,"abstract":"In this paper, we present the PBW-deformations of the smash product $A \\#\nH_{2n^2}$ and the braided tensor product $(A \\otimes^c A^{\\mathrm{op}}_c) \\#\nH_{2n^2}$ for the Kac-Paljutkin type Hopf algebra $H_{2n^2}$ and its Koszul\n$H_{2n^2}$-module algebra $A$. A necessary and sufficient condition for the\nKoszul dual algebra $A^{!}$ to be an $H$-module algebra is given. Then we\nprovide all the PBW-deformations of the smash product algebra $A^! \\# H_{2n^2}$\nfor a given $H_{2n^2}$-module algebra $A$.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"68 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.16557","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we present the PBW-deformations of the smash product $A \#
H_{2n^2}$ and the braided tensor product $(A \otimes^c A^{\mathrm{op}}_c) \#
H_{2n^2}$ for the Kac-Paljutkin type Hopf algebra $H_{2n^2}$ and its Koszul
$H_{2n^2}$-module algebra $A$. A necessary and sufficient condition for the
Koszul dual algebra $A^{!}$ to be an $H$-module algebra is given. Then we
provide all the PBW-deformations of the smash product algebra $A^! \# H_{2n^2}$
for a given $H_{2n^2}$-module algebra $A$.