Multi-parameter deformations of the module of symbols ofdifferential operators

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 ℝv with v ≥ 2, the multi-parameter formal deformations of this module. The space of lin...

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Veröffentlicht in:	International Mathematics Research Notices 2002, Vol.2002 (16), p.847-869
Hauptverfasser:	Agrebaoui, B., Ammar, F., Lecomte, P., Ovsienko, V.
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Sprache:	eng
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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 ℝv with v ≥ 2, the multi-parameter formal deformations of this module. The space of linear differential operators on ℝv provides an important classof such formal deformations; we show, however, that the whole space of deformations is much larger.
doi_str_mv	10.1155/S1073792802101127
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title	Multi-parameter deformations of the module of symbols ofdifferential operators
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