  We study deformations of the standard embedding of the Lie algebra
$\Vect(S^1)$ of smooth vector fields on the circle, into the Lie algebra of
functions on the cotangent bundle $T^*S^1$ (with respect to the Poisson
bracket). We consider two analogous but different problems: (a) formal
deformations of the standard embedding of $\Vect(S^1)$ into the Lie algebra of
functions on $\dot T^*S^1:=T^*S^1\setminusS^1$ which are Laurent polynomials on
fibers, and (b) polynomial deformations of the $\Vect(S^1)$ subalgebra inside
the Lie algebra of formal Laurent series on $\dot T^*S^1$.
