M ay 2 00 2 Hopf Algebras of Dimension 14

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, 55 and 77 is semisimple and thus isomorphic to a group algebra or the dual of a group algebra. We also have some partial results in the classification problem for dimension 16. 0 Introduction In recent years, there has been some progress on the problem of the classification of finite dimensional Hopf algebras over an algebraically closed field of characteristic 0. The first classification discussion appears in [12] for dimensions 4 and 5, but few techniques were then available. In [26], R. Williams classified Hopf algebras of dimension less than 12 by heavily computational methods.