Prime regular Hopf algebras of GK-dimension one

NOTES ON REGULAR MULTIPLIER HOPF ALGEBRAS

In this paper, we associate canonically a precyclic mod- ule to a regular multiplier Hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition

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...