  We propose a q-difference version of the Drinfeld-Sokolov reduction scheme,
which gives us q-deformations of the classical W-algebras by reduction from
Poisson-Lie loop groups. We consider in detail the case of SL(2). The
nontrivial consistency conditions fix the choice of the classical r-matrix
defining the Poisson-Lie structure on the loop group LSL(2), and this leads to
a new elliptic classical r-matrix. The reduced Poisson algebra coincides with
the deformation of the classical Virasoro algebra previously defined in
q-alg/9505025. We also consider a discrete analogue of this Poisson algebra. In
the second part (q-alg/9702016) the construction is generalized to the case of
an arbitrary semisimple Lie algebra.
