Deforming the Lie algebra of vector fields on S1S^1 inside the Poisson algebra on T˙∗S1\dot 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 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 $\dot T^*S^1$.Comment: 19 pages, LaTe

hbar-(Yangian) Deformation of Miura Map and Virasoro Algebra

An hbar-deformed Virasoro Poisson algebra is obtained using the Wakimoto realization of the Sugawara operator for the Yangian double DY_\hbar(sl_2)_c at the critical level c=-2.Comment: LaTeX file, 43kb, No Figures. Serious misprints corrected, one more reference to E. Frenkel adde