Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?

Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur GraphSearch.

Découvrez-en plus sur les applications Graph.

Publication

Special Reductive Groups Over An Arbitrary Field

Mathieu Huruguen
Springer Birkhauser, 2016
Article

A linear algebraic group G defined over a field k is called special if every G-torsor over every field extension of k is trivial. In 1958 Grothendieck classified special groups in the case where the base field is algebraically closed. In this paper we describe the derived subgroup and the coradical of a special reductive group over an arbitrary field k. We also classify special semisimple groups, special reductive groups of inner type, and special quasisplit reductive groups over an arbitrary field k. Finally, we give an application to a conjecture of Serre.

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Concepts associés

Chargement

Publications associées

Chargement

Mathieu Huruguen
Springer Birkhauser, 2016
Article

Résumé

Official source

https://infoscience.epfl.ch/record/225008?ln=fr

À propos de ce résultat

Concepts associés (13)

Concepts associés

Chargement

Publications associées (10)

Publications associées

Chargement

Irreducibility of disconnected subgroups of exceptional algebraic groups

Soumaïa Nadia Ghandour

This dissertation is concerned with the study of irreducible embeddings of simple algebraic groups of exceptional type. It is motivated by the role of such embeddings in the study of positive dimensional closed subgroups of classical algebraic groups. The classification of the maximal closed connected subgroups of simple algebraic groups was carried out by E. B. Dynkin, G. M. Seitz and D. M. Testerman. Their analysis for the classical groups was based primarily on a striking result: if G is a simple algebraic group and ø : G → SL(V ) is a tensor indecomposable irreducible rational representation then, with specified exceptions, the image of G is maximal among closed connected subgroups of one of the classical groups SL(V), Sp(V ) or SO(V ). In the case of closed, not necessarily connected, subgroups of the classical groups, one is interested in considering irreducible embeddings of simple algebraic groups and their automorphism groups: given a simple algebraic group Y defined over an algebraically closed field K, one is led to study the embeddings G < Aut(Y ), where G and Aut(Y ) are closed subgroups of SL(V ) and V is an irreducible rational KY -module on which G acts irreducibly. A partial analysis of such embeddings in the case of classical algebraic groups Y was carried out by B. Ford. We purpose to classify all triples (G, Y, V ) where Y is a simple algebraic group of exceptional type, defined over an algebraically closed field K of characteristic p > 0, G is a closed non-connected positive dimensional subgroup of Y and V is a nontrivial irreducible rational KY -module such that V|G is irreducible. We obtain a precise description of such triples (G, Y, V ).

EPFL2008

Chargement

Irreducibility In Algebraic Groups And Regular Unipotent Elements

Donna Testerman

We study (connected) reductive subgroups G of a reductive algebraic group H, where G contains a regular unipotent element of H. The main result states that G cannot lie in a proper parabolic subgroup of H. This result is new even in the classical case H = SL(n, F), the special linear group over an algebraically closed field, where a regular unipotent element is one whose Jordan normal form consists of a single block. In previous work, Saxl and Seitz (1997) determined the maximal closed positive-dimensional (not necessarily connected) subgroups of simple algebraic groups containing regular unipotent elements. Combining their work with our main result, we classify all reductive subgroups of a simple algebraic group H which contain a regular unipotent element.

2013

Chargement

Restricting representations of classical algebraic groups to maximal subgroups

Mikaël Cavallin

Fix an algebraically closed field

K

having characteristic

p\geq 0

and let

Y

be a simple algebraic group of classical type over

K.

Also let

X

be maximal among closed connected subgroups of

Y

and consider a non-trivial

p

-restricted irreducible rational

KY

-module

V.

In this thesis, we investigate the triples

(Y,X,V)

such that

X

acts with exactly two composition factors on

V

and see how it generalizes a question initially investigated by Dynkin in the

1950

s and then studied by numerous mathematicians. In particular, we study the natural embeddings of

\mbox{SO}_{2n}(K)

in both

\mbox{Spin}_{2n+1}(K)

and

\mbox{SL}_{2n}(K)

and obtain results on the structure of certain Weyl modules.

EPFL2015

Chargement

Extension de corps

En mathématiques, plus particulièrement en algèbre, une extension d'un corps commutatif K est un corps L qui contient K comme sous-corps. Par exemple, le corps ℂ des nombres complexes est une extensi

Sous-groupe

Un sous-groupe est un objet mathématique décrit par la théorie des groupes. Dans cet article, (G, ∗) désigne un groupe d'élément neutre e. Définitions Dans la pratique, on note la loi

Groupe réductif

En mathématiques, un groupe réductif est un groupe algébrique G sur un corps algébriquement clos tel que le radical unipotent de G (c'est-à-dire le sous-groupe des éléments unipotents de ) soit trivia