  We introduce the notion of rational Hopf algebras that we think are able to
describe the superselection symmetries of two dimensional rational quantum
field theories. As an example we show that a six dimensional rational Hopf
algebra $H$ can reproduce the fusion rules, the conformal weights, the quantum
dimensions and the representation of the modular group of the chiral Ising
model. $H$ plays the role of the global symmetry algebra of the chiral Ising
model in the following sense: 1) a simple field algebra $\FA$ and a
representation $\pi$ on $\HS_\pi$ of it is given, which contains the $c=1/2$
unitary representations of the Virasoro algebra as subrepresentations; 2) the
embedding $U\colon H\to\BOH$ is such that the observable algebra $\pi(\OA)^-$
is the invariant subalgebra of $\BOH$ with respect to the left adjoint action
of $H$ and $U(H)$ is the commutant of $\pi(\OA)$; 3) there exist $H$-covariant
primary fields in $\BOH$, which obey generalized Cuntz algebra properties and
intertwine between the inequivalent sectors of the observables.
