Hopf algebras of dimension 2p

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 $H^{\ast }$ 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 $2p$.

6 pages

References in corpus (1)

• Non-semisimple Hopf Algebras of Dimension p^2

Cited by in corpus (8)

• Hopf algebras of dimension pq, II
• Classifying bicrossed products of Hopf algebras
• On Hopf algebras of dimension 4p
• On $4n$-dimensional neither pointed nor semisimple Hopf algebras and the associated weak Hopf algebras
• Block Systems of finite dimensional non-cosemisimple Hopf Algebras
• Quasitriangular Hopf algebras of dimension pq^2
• Hopf algebras of dimension 16
• Admissible Coalgebras and Non-cosemisimple Hopf Algebras