Deforming the Lie algebra of vector fields on $S^1$ inside the Poisson algebra on ${\dot{T}}^{\ast }{S}^1$

V. Ovsienko, C. Roger

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^…