$W_{\infty} Algebra in Two-Dimensional Black Hole

We study the $SL(2;R)/U(1)$ coset model of two-dimensional black hole and its relation to the Liouville theory coupled to c=1 matter. We uncover a basic isomorphism in the algebraic structures of these theories and show that the black hole model has the same physical spectrum as the c=1 model, i.e. tachyons, $W_\infty$ currents and the ground ring elements. we also identify the operator responsible for the creation of the mass of the black hole.