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Radical d'une algèbre symétrique à gauche

Jacques Helmstetter (1979)

Annales de l'institut Fourier

L’étude d’une algèbre symétrique à gauche (de dimension finie sur $C$ ) est liée à celle d’un groupe de transformations affines opérant avec trajectoire ouverte et groupe d’isotropie discret sur cette trajectoire. Son radical est défini grâce aux translations conservant cette trajectoire; l’algèbre est nilpotente si ce groupe opère de façon simplement transitive (les multiplications à droite sont alors nilpotentes). Le radical est le plus grand idéal à gauche nilpotent.

Radix redux: Normal subgroups of symplectic groups.

Douglas L. Costa, Gordon E. Keller (1992)

Journal für die reine und angewandte Mathematik

Rational actions associated to the adjoint representation

Eric M. Friedlander, Brian J. Parshall (1987)

Annales scientifiques de l'École Normale Supérieure

Rational and Generic Cohomology

E. Cline, B. Parshall, L. Scott (1977)

Inventiones mathematicae

Rational fixed points for linear group actions

Pietro Corvaja (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove a version of the Hilbert Irreducibility Theorem for linear algebraic groups. Given a connected linear algebraic group $G$ , an affine variety $V$ and a finite map $π : V \to G$ , all defined over a finitely generated field $κ$ of characteristic zero, Theorem 1.6 provides the natural necessary and sufficient condition under which the set $π (V (κ))$ contains a Zariski dense sub-semigroup $Γ \subset G (κ)$ ; namely, there must exist an unramified covering $p : \tilde{G} \to G$ and a map $θ : \tilde{G} \to V$ such that $π \circ θ = p$ . In the case $κ = ℚ$ , $G = 𝔾_{a}$ is the additive group, we reobtain the...

Rational Homology of Bianchi Groups.

Karen Vogtmann (1985)

Mathematische Annalen

Rational points and Coxeter group actions on the cohomology of toric varieties

Gustav I. Lehrer (2008)

Annales de l’institut Fourier

We derive a simple formula for the action of a finite crystallographic Coxeter group on the cohomology of its associated complex toric variety, using the method of counting rational points over finite fields, and the Hodge structure of the cohomology. Various applications are given, including the determination of the graded multiplicity of the reflection representation.