Fiches de cours

Linear algebraic groups

MATH-479

Enseignant(s) :

Testerman Donna

Langue:

English

Summary

The aim of the course is to establish the main results on the structure of reductive linear algebraic groups defined over an algebraically closed field.

Content

first definitions and properties, morphisms, dimension, Jordan decomposition, tangent space

commutative connected groups, tori, connected solvable groups,

homogeneous spaces and quotients, Borel subgroups,

Lie algebra

root data and structure theorem

Keywords

reductive groups

semisimple

Lie algebra

root data

 

Learning Prerequisites

Recommended courses

Background in group theory, Lie theory and some algebraic geometry

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

Lectures

Expected student activities

exercises and presentations

Assessment methods

Part of the grade will be based upon student presentation of some course material during the exercise sessions or corrected written homework assignments, or both.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Office hours Yes

Resources

Bibliography

Linear Algebraic Groups, J. Humphreys, Springer

Linear Algebraic Groups, T. Springer, Birkhauser

Linear Algebraic Groups, A. Borel, Springer

Linear algebraic groups and finite groups of Lie type, G. Malle and D. Testerman, CUP

 

Références suggérées par la bibliothèque

Dans les plans d'études

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
En construction
 
      Cours
      Exercice, TP
      Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand