# Coursebooks

## Linear algebraic groups

English

#### Remarque

pas donné en 2019-20

#### 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

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:
• Formulate the classification theorem for simple linear algebraic groups
• Construct examples of simple linear algebraic groups
• Prove basic results in the theory

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

### In the programs

• Mathematics - master program, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Oral
• Credits
5
• Subject examined
Linear algebraic groups
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Oral
• Credits
5
• Subject examined
Linear algebraic groups
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 4
• Semester
Spring
• Exam form
Oral
• Credits
5
• Subject examined
Linear algebraic groups
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks

### Reference week

MoTuWeThFr
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
Under construction
Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German