Multi-parameter deformations of the module of symbols ofdifferential operators

The space of symbols of differential operators on a smooth manifold (i.e., the space of symmetric contravariant tensor fields) is naturally a module over the Lie algebra of vector fields. We study, in the case of ℝv with v ≥ 2, the multi-parameter formal deformations of this module. The space of linear differential operators on ℝv provides an important classof such formal deformations; we show, however, that the whole space of deformations is much larger.