Non-semisimple Hopf Algebras of Dimension p²

2001/10/23 by Siu-Hung Ng
Mathematics · #math.QA #math.RA

paper · pdf · doi:10.1016/s0021-8693(02)00139-4

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

arxiv created 2001/10/23 · arxiv updated 2009/11/30

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 p². In particular, if dim H = p², we prove that H is isomorphic to a Taft algebra. We then complete the classification for the Hopf algebras of dimension p².

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