Deformation of vect(1)-modules of symbols

Abstract We consider the action of the Lie algebra of polynomial vector fields, v e c t ( 1 ) , by the Lie derivative on the space of symbols S β n = ⨁ j = 0 n F β − j . We study the deformations of this action. We exhibit explicit expressions of some 2-cocycles generating the second cohomology space H diff 2 ( v e c t ( 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 β n are given. We describe completely the formal deformations for some spaces S β n and we give concrete examples of nontrivial deformations.