Coursebooks

Linear algebraic groups

MATH-479

Lecturer(s) :

Language:

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

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

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

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