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arXiv · 1503.06198

On classification of finite-dimensional semisimple Hopf algebras

Leonid Krop
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Abstract

We develop a mechanism for classication of isomorphism types of non-trivial semisimple Hopf algebras whose group of grouplikes $G(H)$ is abelian of prime index $p$ which is the smallest prime divisor of $|G(H)|$. We describe structure of the second cohomology group of extensions of $\k C_p$ by $\k^G$ where $C_p$ is a cyclic group of order $p$ and $G$ a finite abelian group. We carry out an explicit classification for Hopf algebras of this kind of dimension $p^4$ for any odd prime $p$. The ground field is algebraically closed of characteristic $0$.

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Leonid Krop. 2015-03-20. On classification of finite-dimensional semisimple Hopf algebras. https://arxiv.org/abs/1503.06198

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