We use free field techniques in D = 2 string theory to calculate the perturbation of the special state algebras when the cosmological constant is turned on. In particular, we find that the ''ground cone'' preserved by the ring structure is promoted to 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 interpretation is found. We also quote some facts concerning the Liouville matrix model dictionary in this class of theories.