La propriété de Dixmier pour les algèbres de Lie de champs de vecteurs

Abstract

Given a linear representation $\rho :\mathfrak{g}⟶\mathfrak{g}\ell (V)$ of a Lie algebra $\mathfrak{g}$, one can define a linear representation ${\rho }_m:{\mathfrak{g}}_m⟶\mathfrak{g}\ell (V^m)$ of the generalized Takiff algebra ${\mathfrak{g}}_m$. It is proved here that the vector fields defined by ${\rho }_m$ on $V^m$ do have the Dixmier property if those defined by $\rho$ have the same property. Examples where the result applies are given and in particular, those of the adjoint or coadjoint representations of Takiff algebras.

arXiv commentThis article is written in french with an english abstract