PBW-deformations of smash products involving Hopf algebra of Kac-Paljutkin type
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917098984308736 |
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| author | Gao, Yujie Yang, Shilin |
| author_facet | Gao, Yujie Yang, Shilin |
| contents | Let $H_{2n^2}$ be the Kac-Paljutkin type Hopf algebra of dimension $2n^2$, $A$ its graded Koszul Artin-Schelter regular $H_{2n^2}$-module algebra of dimension $2$, $A^!$ the Koszul dual of $A$, and $A^{\mathrm{op}}_c$ the braided-opposite algebra of $A$. This paper describes $(0, 1)$-degree PBW-deformations of the smash product $A \sharp H_{2n^2}$ and those of $A^! \sharp\, H_{2n^2}$ under the condition that the Koszul dual $A^!$ of $A$ is also an $H_{2n^2}$-module algebra. Also, $0$-degree PBW-deformations of $(A \otimes^c A^{\mathrm{op}}_c) \sharp\, H_{2n^2}$ are explored, where $A \otimes^c A^{\mathrm{op}}_c$ is the associated braided tensor product algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16557 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | PBW-deformations of smash products involving Hopf algebra of Kac-Paljutkin type Gao, Yujie Yang, Shilin Rings and Algebras Quantum Algebra Representation Theory 16S37, 16S40, 16S80 Let $H_{2n^2}$ be the Kac-Paljutkin type Hopf algebra of dimension $2n^2$, $A$ its graded Koszul Artin-Schelter regular $H_{2n^2}$-module algebra of dimension $2$, $A^!$ the Koszul dual of $A$, and $A^{\mathrm{op}}_c$ the braided-opposite algebra of $A$. This paper describes $(0, 1)$-degree PBW-deformations of the smash product $A \sharp H_{2n^2}$ and those of $A^! \sharp\, H_{2n^2}$ under the condition that the Koszul dual $A^!$ of $A$ is also an $H_{2n^2}$-module algebra. Also, $0$-degree PBW-deformations of $(A \otimes^c A^{\mathrm{op}}_c) \sharp\, H_{2n^2}$ are explored, where $A \otimes^c A^{\mathrm{op}}_c$ is the associated braided tensor product algebra. |
| title | PBW-deformations of smash products involving Hopf algebra of Kac-Paljutkin type |
| topic | Rings and Algebras Quantum Algebra Representation Theory 16S37, 16S40, 16S80 |
| url | https://arxiv.org/abs/2408.16557 |