  In this paper we employ the construction of Dirac bracket for the remaining
current of $sl(2)_q$ deformed Kac-Moody algebra when constraints similar to
those connecting the $sl(2)$-WZW model and the Liouville theory are imposed and
show that it satisfy the q-Virasoro algebra proposed by Frenkel and
Reshetikhin. The crucial assumption considered in our calculation is the
existence of a classical Poisson bracket algebra induced, in a consistent
manner by the correspondence principle, mapping the quantum generators into
commuting objects of classical nature preserving their algebra.
