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Non-semisimple Hopf Algebras of Dimension p^2

Siu-Hung Ng
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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.

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Siu-Hung Ng. 2001-10-23. Non-semisimple Hopf Algebras of Dimension p^2. https://doi.org/10.1016/s0021-8693(02)00139-4

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