%0 Journal Article %T Equivalence of BRST cohomologies for 2-d black hole and c=1 Liouville theory %A Hiroshi Ishikawa %A Mitsuhiro Kato %J Physics %D 1992 %I arXiv %R 10.1016/0370-2693(93)90386-V %X We study the relation between the $SL(2,R)/U(1)$ black hole and the $c=1$ Liouville theory. A deformation, which interpolates the BRST operators of both models, is explicitly constructed. This interpolation is isomorphic, and the physical spectrum of the black hole is equivalent to that of the $c=1$ model tensored by a topological $U(1)/U(1)$ model. Some implications of the deformation are discussed. %U http://arxiv.org/abs/hep-th/9211080v1