The exchange algebra for Liouville theory on a punctured Riemann sphere

We consider in this paper the classical Liouville field theory of the Riemann sphere with n punctures. In terms of the uniformization theorem of the Riemann surface, we explicitly show the classical exchange algebra (CEA) for the chiral components of the Liouville field. We find that the matrix which dominates the CEA is related to the symmetry of the Lie group SL(n) in a nontrivial manner with n>3. (orig.)