INTEGRABLE EXTENSIONS OF THE RATIONAL AND TRIGONOMETRIC A(N) CALOGERO-MOSER POTENTIALS

We describe the R-matrix structure associated with integrable extensio ns, containing both one-body and two-body potentials, of the A(N) Calo gero-Moser N-body systems. We construct non-linear, finite dimensional Poisson algebras of observables. Their N --> infinity limits realize the infinite Lie algebras Sdiff(R x S1) in the trigonometric case and Sdiff(R2) in the rational case. It is then isomorphic to the algebra o f observables constructed in the two-dimensional collective string fie ld theory.