On Graded Global Dimension of Color Hopf Algebras

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...

Graded Hopf Algebras and Pairings

We study positively-graded Hopf algebras and obtain (dual) Gabriel-type results on graded Hopf algebras. Using it, we get certain (non-degenerate) graded Hopf pairings between quantum symmetric algebras.

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

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.