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(S2p) = p2d where d ≡ pq (mod 4). As a consequence, if p, q are twin primes, then any Hopf algebra of dimension pq is semisimple. © 2004 Elsevier Inc. All rights reserved.
Publication Source (Journal or Book title)
Journal of Algebra
Ng, S. (2004). Hopf algebras of dimension pq. Journal of Algebra, 276 (1), 399-406. https://doi.org/10.1016/j.jalgebra.2003.11.008