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The Development of a New Matrix Operator and its Application to the Study of Nonlinear Coupled Wave Equations

Authors:	Darbyshire P M Hall T J

Institution:	(1) Département de Mathématiques, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France;(2) Faculté des Sciences de Sfax, Département de Mathématiques, Route de Soukra, 3038 Sfax, Tunisia

Abstract:	In this Letter, we consider Kontsevich's wheel operators for linear Poisson structures, i.e. on the dual of Lie algebras $\mathfrak{g}$ . We prove that these operators vanish on each invariant polynomial function on $\mathfrak{g}$ *. This gives a characterization of the Kontsevich star products which are deformations relative to the algebra of invariant functions.

Keywords:	deformation quantization Lie algebras invariant
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