Hopf algebras of dimension 2p

Details Hopf algebras of dimension 2p Hopf algebras of dimension 2p

2003-11-17

arxiv.org/abs/math/0311291v2

Proc. Amer. Math. Soc. 133 (2005), 2237-2242

Mathematics

Quantum Algebra

6 pages

Scientific paper

10.1090/S0002-9939-05-07804-4

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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