  We pose a representation-theoretic question motivated by an attempt to
resolve the Andrews-Curtis conjecture. Roughly, is there a triangular Hopf
algebra with a collection of self-dual irreducible representations $V_i$ so
that the product of any two decomposes as a sum of copies of the $V_i$, and
$\sum (\rank V_i)^2=0$? This data can be used to construct a `topological
quantum field theory' on 2-complexes which stands a good chance of detecting
counterexamples to the conjecture.
