Semisimple Hopf algebras of dimension $2q^3$

Jingcheng Dong; Li Dai

Semisimple Hopf algebras of dimension $2q^3$

Rings and Algebras 2012-04-06 v3

Authors: Jingcheng Dong , Li Dai

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 $q^3$ .

Keywords

semisimple Hopf algebra dimension 2q^3 Radford biproduct Yetter-Drinfeld module group algebra Hopf algebra extension

Cite

@article{arxiv.1105.4398,
  title  = {Semisimple Hopf algebras of dimension $2q^3$},
  author = {Jingcheng Dong and Li Dai},
  journal= {arXiv preprint arXiv:1105.4398},
  year   = {2012}
}

Comments

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

Semisimple Hopf algebras of dimension $2q^3$

Abstract

Keywords

Cite

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