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

2009/11/20 by Mustapha Raïs, Raïs, Mustapha
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.0911.3993

This article is written in french with an english abstract

arxiv created 2009/11/20 · openalex publication_date 2009/11/20 · arxiv updated 2009/12/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Given a linear representation ρ: \mathfrakg \longrightarrow \mathfrakgℓ(V) of a Lie algebra \mathfrakg, one can define a linear representation ρ_m : \mathfrakg_m \longrightarrow \mathfrakgℓ(V^m) of the generalized Takiff algebra \mathfrakg_m. It is proved here that the vector fields defined by ρ_m on V^m do have the Dixmier property if those defined by ρ have the same property. Examples where the result applies are given and in particular, those of the adjoint or coadjoint representations of Takiff algebras.

Related

• Takiff algebras with polynomial rings of symmetric invariants
• The representation theory of Brauer categories II: curried algebra
• Vector fields invariant under a linear action of a compact Lie group
• Linear degenerations of algebras and certain representations of the general linear group
• Dixmier's Problem 6 for the Weyl Algebra (the Generic type Problem)