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arXiv · 1712.00826

On Hopf algebras over the unique $12$-dimensional Hopf algebra without the dual Chevalley property

Rongchuan Xiong
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Abstract

Let $\mathds{k}$ be an algebraically closed field of characteristic zero. We determine all finite-dimensional Hopf algebras over $\mathds{k}$ whose Hopf coradical is isomorphic to the unique $12$-dimensional Hopf algebra $\mathcal{C}$ without the dual Chevalley property, such that the diagrams are strictly graded and the corresponding infinitesimal braidings are indecomposable objects in ${}_{\mathcal{C}}^{\mathcal{C}}\mathcal{YD}$. In particular, we obtain new Nichols algebras of dimension $18$ and $36$ and two families of new Hopf algebras of dimension $216$.

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BibTeXRIS

Rongchuan Xiong. 2017-12-03. On Hopf algebras over the unique $12$-dimensional Hopf algebra without the dual Chevalley property. https://arxiv.org/abs/1712.00826

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