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 integer n, then H or H * is not unimodular. Using this result, we prove that if dim(H) = 2p for some odd prime p, then H is semisimple. This completes the classification of Hopf algebras of dimension 2p. In recent years, there has been some progr...

Let H be a cosemisimple Hopf algebra over an algebraically closed field k. Assume that H contains a simple subcoalgebra of dimension 9. We show that if H has no simple subcoalgebras of even dimension then H contains either a grouplike element with order 2 or 3, a Hopf subalgebra of dimension 75, or a family of simple subcoalgebras whose dimensions are the squares of each positive odd integer. I...

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...

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E6, E7, F4, G2, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character.

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E6, E7, F4, G2, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character.

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 65–94. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character.

Let L be a field which is a Galois extension of the field K with Galois group G. Greither and Pareigis [GP87] showed that for many G there exist K-Hopf algebras H other than the group ring KG which make L into an H-Hopf Galois extension of K (or a Galois H∗object in the sense of Chase and Sweedler [CS69]). Using Galois descent they translated the problem of determining the Hopf Galois structure...

Let k be an algebraically closed field of characteristic p > 0. The purpose of this paper is to describe the Hopf algebra of a finite commutative infinitesimal unipotent k-group scheme which is uniserial, i.e., which has a unique composition series. As there is only one simple finite commutative infinitesimal unipotent group scheme (namely αp := ker {F : Ga → Ga} , with Ga being the additive gr...

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 29–46. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character.