Multi-parameter deformations of the module of symbols of differential operators

Abstract

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 ${\mathbf{R}}^{\mathbf{n}}$ with $n\ge 2$, multi-parameter formal deformations of this module. The space of linear differential operators on ${\mathbf{R}}^{\mathbf{n}}$ provides an important class of such formal deformations; we show, however, that the whole space of deformations is much larger.

17 pages, LaTeX