Mathematics – Representation Theory
Scientific paper
2009-11-20
Mathematics
Representation Theory
This article is written in french with an english abstract
Scientific paper
Given a linear representation $\rho : \mathfrak{g} \longrightarrow \mathfrak{g}\ell(V)$ of a Lie algebra $\mathfrak{g}$, one can define a linear representation $\rho_m : \mathfrak{g}_m \longrightarrow \mathfrak{g}\ell(V^m)$ 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.
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