We develop a mechanism for classication of isomorphism types of non-trivialsemisimple Hopf algebras whose group of grouplikes $G(H)$ is abelian of primeindex $p$ which is the smallest prime divisor of $|G(H)|$. We describestructure 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. Wecarry out an explicit classification for Hopf algebras of this kind ofdimension $p^4$ for any odd prime $p$. The ground field is algebraically closedof characteristic $0$.
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机译：我们开发了一种非平凡的半简单Hopf代数的同构类型经典化的机制，该类的群像$ G（H）$是素数索引$ p $的阿贝尔数，这是$ | G（H）| $的最小素数。我们描述了由$ \ k ^ G $扩展的第二个同调扩展群，其中$ C_p $是阶次$ p $的循环群，而$ G $是有限阿贝尔群。对于任何奇数质数$ p $，我们都会对此类维$ p ^ 4 $的Hopf代数进行显式分类。地场是代数闭合的特征$ 0 $。
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