Deforming the Lie algebra of vector fields on S-1 inside the Poisson algebra on T*S-1

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 con sider two analogous but different problems: (a) formal deformations of the standard embedding of Vect(S') into the Lie algebra of functions on (T) ove r dot* S-1 := T*S-1\S-1 which are Laurent polynomials on fibers, and (b) po lynomial deformations of the Vect(S') subalgebra inside the Lie algebra of formal Laurent series on (T) over dot S-1.