Hopf algebras of dimension 2𝑝

Ng, Siu-Hung

doi:10.1090/S0002-9939-05-07804-4

Hopf algebras of dimension $2p$
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Proc. Amer. Math. Soc. 133 (2005), 2237-2242 Request permission

Abstract:

Let $H$ be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If $H$ is not semisimple and $\dim (H)=2n$ for some odd integer $n$, then $H$ or $H^*$ is not unimodular. Using this result, we prove that if $\dim (H)=2p$ for some odd prime $p$, then $H$ is semisimple. This completes the classification of Hopf algebras of dimension $2p$.

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