  The goal of this paper is to classify ``finite subgroups in U_q sl(2)'' where
$q=e^{\pi\i/l}$ is a root of unity. We propose a definition of such a subgroup
in terms of the category of representations of U_q sl(2); we show that this
definition is a natural generalization of the notion of a subgroup in a
reductive group, and that it is also related with extensions of the chiral
(vertex operator) algebra corresponding to sl^(2) at level k=l-2. We show that
``finite subgroups in U_q sl(2)'' are classified by Dynkin diagrams of types
A_n, D_{2n}, E_6, E_8 with Coxeter number equal to $l$, give a description of
this correspondence similar to the classical McKay correspondence, and discuss
relation with modular invariants in (sl(2))_k conformal field theory.
