Discriminants et sommes de carrés
In this paper we generalize the notion of discriminant for symmetric matrices and some results about it to the case of symmetric spaces.
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arXiv subjects
Mustapha Raïs
Publications and source records attributed to Mustapha Raïs.
La propriété de Dixmier pour les algèbres de Lie de champs de vecteurs
Given a linear representation $ρ: \mathfrak{g} \longrightarrow \mathfrak{g}\ell(V)$ of a Lie algebra $\mathfrak{g}$, one can define a linear representation $ρ_m : \mathfrak{g}_m \longrightarrow \mathfrak{g}\ell(V^m)$ of the generalized Takiff algebra $\mathfrak{g}_m$. It is proved here that the vector fields defined by $ρ_m$ 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.
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Les invariants polynômes de la représentation coadjointe de groupes inhomogènes
Explicit generators are given for the ring of invariant polynomials under the coadjoint representation of certain inhomogeneous groups.
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Notes sur l'indice des algèbres de Lie (I)
This article contains: - Proofs of certain results recently obtained by D. Panyushev. - An addendum to the "inequality of Panyushev". - Calculations of indexes of certain contracted Lie algebras. - Examples of additivity of the index of Lie algebras. ----- On trouvera dans ce papier : - Des démonstrations de certains des résultats obtenus récemment par D. Panyushev. - Un complément portant sur "l'inégalité de Panyushev''. - Des calculs d'indices de certaines contractées d'algèbres de Lie. - Des exemples d'additivité de l'indice des algèbres de Lie.
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Notes sur l'indice des algèbres de Lie (II)
This text is a continuation to "Notes sur l'indice des algèbres de Lie (I)", math.RT/0605499 ----- Ce texte est une suite à : "Notes sur l'indice des algèbres de Lie (I)".
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Note sur les invariants du groupe affine
In the paper, it is proved that any $C^{1}$-function on GL(n) which is locally $P$-invariant (here $P$ is the affine (sub)group of GL(n)) is locally $G$-invairant. There is also a statement for distributions (a very weak form of Baruch's results).
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Notes sur la notion d'invariant caractéristique
Let $G$ be a Lie group acting on a vector space $V$. Given a set of $G$-invariants, one can ask the question : does this set of invariants characterize the group $G$ ? We recall here some known results, ask questions and state some conjectures for different choices of invariants : polynomial functions, orbits, distributions, and different types of groups.
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