Semisimple Hopf algebras of dimension $2q³$

Year, pages: 2015, 53 - 62

Let $q$ be a prime number, $k$ an algebraically closed field of characteristic $0$, and $H$ a non-trivial semisimple Hopf algebra of dimension $2q³$. 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 $q³$.

Dong, J., Dai, L. 2015. Semisimple Hopf algebras of dimension $2q³$. In Mathematica Slovaca, vol. 65, no.1, pp. 53-62. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0006

Dong, J., Dai, L. (2015). Semisimple Hopf algebras of dimension $2q³$. Mathematica Slovaca, 65(1), 53-62. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0006