Hopf algebras of dimension 14

Details Hopf algebras of dimension 14 Hopf algebras of dimension 14

2002-05-23

arxiv.org/abs/math/0205243v2

Mathematics

Quantum Algebra

16 pages. The revised version of this paper includes a proof that Hopf algebras of dimension 65 are semisimple, a dimension no

Scientific paper

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

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