We study non-trivial deformations of the natural action of the Lie algebra Vect(R n ) on the space of differential forms on R n . We calculate abstractions for integrability of infinitesimal multi-parameter deformations and determine the commutative associative algebra corresponding to the miniversal deformation in the sense of [3].

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Abstract. We consider the action of Vect Pol (R) by Lie derivative on the spaces of symbols of differential operators. We study the deformations of this action that become trivial once restricted to sl(2). Necessary and sufficient conditions for integrability of infinitesimal deformations are given.

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We consider the action of the Lie algebra of polynomial vector fields, vect(1), by the Lie derivative on the space of symbols S n δ = n j=0 F δ−j . We study deformations of this action. We exhibit explicit expressions of some 2-cocycles generating the second cohomology space H 2 diff (vect(1), D ν,µ ) where D ν,µ is the space of differential operators from F ν to F µ . Necessary second-order integrability conditions of any infinitesimal deformations of S n δ are given. We describe completely the formal deformations for some spaces S n δ and we give concrete examples of non trivial deformations.