2002/05/23 by M. Beattie, Beattie, M., S. Dăscălescu +1
Mathematics · #16W30 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16W30
paper · pdf · doi:10.48550/arxiv.math/0205243
16 pages. The revised version of this paper includes a proof that Hopf algebras of dimension 65 are semisimple, a dimension not covered so far in the literature
arxiv created 2003/04/21 · arxiv updated 2009/11/30
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 H1, 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.