  We describe the $R$-matrix structure associated with integrable extensions,
containing both one-body and two-body potentials, of the $A_N$ Calogero-Moser
$N$-body systems. We construct non-linear, finite dimensional Poisson algebras
of observables. Their $N
  \rightarrow \infty$ limit realize the infinite Lie algebras Sdiff$({\Bbb R}
\times S_1 )$ in the trigonometric case and
  Sdiff$({\Bbb R }^2)$ in the rational case. It is then isomorphic to the
algebra of observables constructed in the two-dimensional collective string
field theory.
