Semisimple Hopf algebras of dimension $2q^3$

Abstract

Let $q$ be a prime number, $k$ an algebraically closed field of characteristic 0, and $H$ a non-trivial semisimple Hopf algebra of dimension $2q^3$. This paper proves that $H$ can be constructed either from group algebras and their duals by means of extensions, or from Radford's biproduct $H\cong R#kG$, where $kG$ is the group algebra of $G$ of order 2, $R$ is a semisimple Yetter-Drinfeld Hopf algebra in ${}^{kG}_{kG}\mathcal{YD}$ of dimension $q^3$.

I come back! It's a misunderstanding! There is no mistakes in this paper. arXiv admin note: substantial text overlap with arXiv:1110.2273, arXiv:1101.1568, arXiv:1009.3541, arXiv:1103.5117 arXiv:1102.3770