{"title":"涉及 Kac-Paljutkin 型霍普夫代数的粉碎积的 PBW 变形","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":"{\"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}","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}
PBW-deformations of smash products involving Hopf algebra of Kac-Paljutkin type
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 $A$.
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