Multi-parameter deformations of the module of symbols ofdifferential operators

By B. Agrebaoui, F. Ammar, P. Lecomte, Valentin Ovsienko. 2000

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a5b25265222eb394453a42b6b455f584451e6135