Hopf algebras of prime dimension in positive characteristic

Hopf Algebras of Dimension

Let H be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If H is not semisimple and dim(H) = 2n for some odd integers n, then H or H * is not unimodular. Using this result, we prove that if dim(H) = 2p for some odd primes p, then H is semisimple. This completes the classification of Hopf algebras of dimension 2p. In recent years, there has been some pro...

On Hopf algebras of dimension

Hopf Algebras of Dimension p

Let p be a prime number. It is known that any non-semisimple Hopf algebra of dimension p over an algebraically closed field of characteristic 0 is isomorphic to a Taft algebra. In this exposition, we will give a more direct alternative proof to this result.

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 is semisimple and thus isomorphic to a group algebra or...

Hopf Galois Extensions, Triangular Structures, and Frobenius Lie Algebras in Prime Characteristic

The final goal of this paper is to introduce certain finite dimensional Hopf algebras associated with restricted Frobenius Lie algebras over a field of characteristic p > 0. The antipodes of these Hopf algebras have order either 2p or 2, and in the minimal dimension p there exists just one Hopf algebra in this class which coincides with an example due to Radford [35] of a Hopf algebra with a no...