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

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

2000-11-08

arxiv.org/abs/math/0011048v1

Mathematics

Quantum Algebra

17 pages, LaTeX

Scientific paper

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.

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