  We use free field techniques in D=2 string theory to calculate the
perturbation of the special state algebras when the cosmologi- cal constant is
turned on. In particular, we find that the "ground cone" preserved by the ring
structure is promoted to a three dimen- sional hyperboloid as conjectured by
Witten. On the other hand, the perturbed (1,1) a three dimensional hyperboloid
as conjectured by Witten. On the other hand, the perturbed (1,1) current
algebra of moduli deformations is computed completely, and no simple
geometrical inter- pretation is found. We also quote some facts concerning the
Liouville/matrix model dictio- nary in this class of theories.
