Hopf Algebras of Dimension pq

2003/04/30 by Siu-Hung Ng
Mathematics · #math.QA #math.RA #msc:16W30

paper · pdf · doi:10.1016/j.jalgebra.2003.11.008

published as Journal of Algebra, 276 (2004), no. 1, 399--406. · minor change of version 1; manuscript of the talk at the special session of AMS meeting (#986) at New York, April, 2003

arxiv created 2003/05/07 · arxiv updated 2009/11/30

Abstract

Let H be a non-semisimple Hopf algebra with antipode S of dimension pq over an algebraically closed field of characteristic 0 where p ≤ q are odd primes. We prove that \Tr(S^2p)=p²d where d ≡ pq \pmod4. As a consequence, if p,q are twin primes, then any Hopf algebra of dimension pq is semisimple.

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