Abstract :
Let H be a finite-dimensional Hopf algebra with antipode S of dimension pq over an algebraically closed field of characteristic 0, where p q are odd primes. If H is not semisimple, then the order of S4 is p, and Tr(S2p) is an integer divisible by p2. In particular, if dimH=p2, we prove that H is isomorphic to a Taft algebra. This completes the classification for the Hopf algebras of dimension p2.
