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arXiv · 1911.05516

Finite-dimensional Hopf algebras over the Hopf algebra $H_{b:1}$ of Kashina

Yiwei Zheng·Yun Gao·Naihong Hu
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Abstract

Let $H$ be the 16-dimensional nontrivial (namely, noncommutative and noncocommutative) semisimple Hopf algebra $H_{b:1}$ appeared in Kashina's work \cite{K00}. We obtain all simple Yetter-Drinfeld modules over $H$ and then determine all finite-dimensional Nichols algebras satisfying $\mathcal{B}(V)\cong \bigotimes_{i\in I}\mathcal{B}(V_i)$, where $V=\bigoplus_{i\in I}V_i$, each $V_i$ is a simple object in $_H^H\mathcal{YD}$. Finally, we describe all liftings of those $\mathcal{B}(V)$ over $H$.

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Yiwei Zheng, Yun Gao, Naihong Hu. 2019-11-13. Finite-dimensional Hopf algebras over the Hopf algebra $H_{b:1}$ of Kashina. https://doi.org/10.1016/j.jalgebra.2020.09.035

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