  The orbifold CFT dual to string theory on $ADS_3 \times S^3$ allows a
construction of gravitational actions based on collective field techniques. We
describe a fundamental role played by a Lie algebra constructed from chiral
primaries and their CFT conjugates. The leading terms in the algebra at large
$N$ are derived from the computation of chiral primary correlation functions.
The algebra is argued to determine the dynamics of the theory, its
representations provide free and interacting hamiltonians for chiral primaries.
This dynamics is seen to be given by an effective one plus one dimensional
field theory. The structure of the algebra and its representations shows
qualitatively new features associated with thresholds at $L_0= N$, $ L_0 = N/2$
and $L_0=N/4$, which are related to the stringy exclusion principle and to
black holes. We observe relations between fusion rules of $SU_q(2|1,1)$ for $q
= e^{i \pi / {N+1}} $, and the correlation functions, which provide further
evidence for a non-commutative spacetime.
