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On some classification of finite-dimensional Hopf algebras over the Hopf algebra $H_{b:1}^*$ of Kashina
- Source :
- Comm. Algebra 51 (1) (2023)
- Publication Year :
- 2022
-
Abstract
- Let $H$ be the dual of $16$-dimensional nontrivial semisimple Hopf algebra $H_{b:1}$ in the classification work of Kashina \cite{K00}. We completely determine all finite-dimensional Nichols algebras satisfying $\mathcal{B}(N)\cong \bigotimes_{i\in I}\mathcal{B}(N_i)$, where $N=\bigoplus_{i\in I}N_i$, each $N_i$ is a simple object in $_H^H\mathcal{YD}$. Under this assumption, we classify all those Hopf algebras of finite-dimensional growth from the semisimple Hopf algebra $H$ via the relevant Nichols algebras $\mathcal B(N)$.<br />Comment: 22 pages
- Subjects :
- Mathematics - Quantum Algebra
16T05, 16T99
Subjects
Details
- Database :
- arXiv
- Journal :
- Comm. Algebra 51 (1) (2023)
- Publication Type :
- Report
- Accession number :
- edsarx.2209.12470
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1080/00927872.2022.2099551