Coursebooks

Topics in the theory of reductive algebraic groups, Lie algebras, and representation theory I (2019)

MATH-620(1)

Lecturer(s) :

Testerman Donna

Language:

English

Frequency

Every year

Remarque

Every year. Next time: Fall 2019

Summary

The topics addressed in this course are the structure theory of eductive algebraic groups, their associated Lie algebras, the related finite groups of Lie type, and the representation theory of all of these objects.

Content

We start with the basic structure theory of reductive algebraic groups and proceed to study:

 

their representations, the subgroup structure, conjugacy classes, structural results on their Lie algebras,
the related finite groups of Lie type, generation problems.
The working group is based on advanced textbooks and journal articles.

Keywords

semisimple, reductive, algebraic groups, Lie algebras

Learning Prerequisites

Required courses

Advanced abstract algebra and group theory, representation theory, preferably some knowledge of Lie theory.

In the programs

    • Semester
    • Exam form
       Oral presentation
    • Credits
      3
    • Subject examined
      Topics in the theory of reductive algebraic groups, Lie algebras, and representation theory I (2019)
    • Lecture
      28 Hour(s)
    • Exercises
      14 Hour(s)
    • Practical work
      14 Hour(s)

Reference week

 
      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