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Deformation of \(\mathfrak{vect}(1)\)-modules of symbols. (English) Zbl 1195.47048

This paper deals with the deformations of the action of \(\mathfrak{vect}(1)\), the Lie algebra of polynomial vector fields, by the Lie derivative, on the space of symbols. The authors restrict themselves to differential operators. They give all the second order integrability conditions and also the second order term of any formal deformation. They finally describe completely the formal deformations for some spaces and study explicitly concrete examples of nontrivial deformations.

MSC:

47L15 Operator algebras with symbol structure
53D55 Deformation quantization, star products
53D17 Poisson manifolds; Poisson groupoids and algebroids
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References:

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