Survey on Hopf algebras of GK-dimension 1 and 2

On Hopf algebras of dimension

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 semisimple Hopf algebras of low dimension

We announce recent progress on the question about the semisolvability of semisimple Hopf algebras of dimension < 60. 2000 AMS Subject Classification: 16W30

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...

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.