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

Ammar, F.; Agrebaoui, B.; Ovsienko, V.

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

Authors

Ammar, F.

Agrebaoui, B.

Ovsienko, V.

Description

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 $\bf R^n$ with $n\geq2$, multi-parameter formal deformations of this module. The space of linear differential operators on $\bf R^n$ provides an important class of such formal deformations; we show, however, that the whole space of deformations is much larger.
17 pages, LaTeX