# Coursebooks

## Linear algebraic groups

#### Lecturer(s) :

Urech Christian Lucius

English

#### Summary

The aim of the course is to give an introduction to linear algebraic groups over algebraically closed fields and to give an insight into a beautiful subject that combines algebraic geometry with group theory.

#### Content

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

commutative connected groups, tori, connected solvable groups,

Lie algebra

group actions on algebraic varieties and some invariant theory

#### Keywords

algebraic groups

group actions on algebraic varieties

Lie algebra

algebraic geometry

group theory

#### Learning Prerequisites

##### Required courses

at least one introductory algebraic geometry course, group theory

##### 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:
• State the most important notions and results
• Construct examples
• Prove basic results in the theory

#### Teaching methods

Lectures and exercises

#### 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 Assistants Yes Forum 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, 2020-2021, 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, 2020-2021, 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, 2020-2021, 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