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arXiv · 1510.02645

On semisimple Hopf algebras of dimension $2^{m}$, II

Yevgenia Kashina
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Abstract

In this paper we classify, up to equivalence, all semisimple nontrivial Hopf algebras of dimension $2^{2n+1}$ for $n\geq 2$ over an algebraically closed field of characteristic $0$ with the group of group-like elements isomorphic to $\mathbb{Z}_{2^{n}}\times \mathbb{Z}_{2^{n}}$. Moreover we classify all such nonisomorphic Hopf algebras of dimension $32$ and show that they are not twist-equivalent to each other. More generally, given an abelian group of order $2^{m-1}$ we give an upper bound for the number of nonisomorphic nontrivial Hopf algebras of dimension $2^{m}$ which have this group as their group of group-like elements.

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Yevgenia Kashina. 2015-10-09. On semisimple Hopf algebras of dimension $2^{m}$, II. https://arxiv.org/abs/1510.02645

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