Non-semisimple Hopf Algebras of Dimension p^2

Details Non-semisimple Hopf Algebras of Dimension p^2 Non-semisimple Hopf Algebras of Dimension p^2

2001-10-19

arxiv.org/abs/math/0110223v2

(Corrected version) Journal of Algebra 255 (2002) 182-197

Mathematics

Quantum Algebra

Scientific paper

10.1016/S0021-8693(02)00139-4

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.

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