Hopf Algebras of Dimension $pq$

Details Hopf Algebras of Dimension $pq$ Hopf Algebras of Dimension $pq$

2003-04-12

arxiv.org/abs/math/0304156v2

Journal of Algebra, 276 (2004), no. 1, 399--406.

Mathematics

Quantum Algebra

minor change of version 1; manuscript of the talk at the special session of AMS meeting (#986) at New York, April, 2003

Scientific paper

10.1016/j.jalgebra.2003.11.008

Let $H$ be a non-semisimple Hopf algebra with antipode $S$ of dimension $pq$
over an algebraically closed field of characteristic 0 where $p \le q$ are odd
primes. We prove that $\Tr(S^{2p})=p^2d$ where $d \equiv pq \pmod{4}$. As a
consequence, if $p,q$ are twin primes, then any Hopf algebra of dimension $pq$
is semisimple.

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