Non-semisimple Hopf Algebras of Dimension p^2
Quantum Algebra
2007-05-23 v2 Rings and Algebras
Abstract
Let H be a Hopf algebra of dimension pq over an algebraically closed field of characteristic 0, where p <= q are odd primes. Suppose that S is the antipode of H. If H is not semisimple, then S^{4p}=id_H and Tr(S^{2p}) is an integer divisible by p^2. In particular, if dim H = p^2, we prove that H is isomorphic to a Taft algebra. We then complete the classification for the Hopf algebras of dimension p^2.
Cite
@article{arxiv.math/0110223,
title = {Non-semisimple Hopf Algebras of Dimension p^2},
author = {Siu-Hung Ng},
journal= {arXiv preprint arXiv:math/0110223},
year = {2007}
}