  An analytic expression is proposed for the three-point function of the
exponential fields in the Liouville field theory on a sphere. In the classical
limit it coincides with what the classical Liouville theory predicts. Using
this function as the structure constant of the operator algebra we construct
the four-point function of the exponential fields and verify numerically that
it satisfies the conformal bootstrap equations, i.e., that the operator algebra
thus defined is associative. We consider also the Liouville reflection
amplitude which follows explicitly from the structure constants.
