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Hopf algebras of dimension 14

M. Beattie·S. Dăscălescu
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Abstract

Let H be a finite dimensional non-semisimple Hopf algebra over an algebraically closed field k of characteristic 0. If H has no nontrivial skew-primitive elements, we find some bounds for the dimension of H_1, the second term in the coradical filtration of H. Using these results, we are able to show that every Hopf algebra of dimension 14 is semisimple and thus isomorphic to a group algebra or the dual of a group algebra. Also a Hopf algebra of dimension pq where p and q are odd primes with p<q and q less than or equal to 1 + 3p, and also less than or equal to 13, is semisimple and thus a group algebra or the dual of a group algebra. We also have some partial results in the classification problem for dimension 16.

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BibTeXRIS

M. Beattie, S. Dăscălescu. 2003-04-21. Hopf algebras of dimension 14. https://arxiv.org/abs/math/0205243

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