Lie Algebras
Liealgebror

FMA095F, 6 credits

Valid from: Autumn 2013
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-01-27

General Information

Division: Mathematics
Course type: Third-cycle course
Teaching language: English

Aim

The course is established to give a preparation for research within the theory of Lie algebras and groups; geometric mechanics; and theoretical physics.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must be able to reproduce key results and sketch their proofs.

Competences and Skills

For a passing grade the doctoral student must

• be able to compare key results.
• be able to apply the basic techniques, results and concepts of the course to concrete examples and exercises.

Course Contents

Basic definitions and examples. Structure theory of Lie Algebras. Correspondence between Lie Groups and Lie Algebras. Universal enveloping algebra. Semisimple Lie Algebras. Solvable and Nilpotent Lie Algebras. Root systems. Representations. Theory of highest weights.

Course Literature

• Humphreys, J. E.: Introduction to Lie Algebras and Representation Theory. Springer, 1978. ISBN 0387900535.
• Kaplansky: Lie algebras and locally compact groups. 1995. ISBN 9780226424538.

One of the books is used, possibly with complementary hand-outs.

Instruction Details

Types of instruction: Lectures, exercises

Examination Details

Examination formats: Written exam, oral exam
Grading scale: Failed, pass
Examiner:

Admission Details

Assumed prior knowledge: FMAF05 Systems and transforms and FMA200 Algebraic structures, or the corresponding knowledge.

Further Information

The course will be given if there are at least six applicants.

Course Occasion Information

Contact and Other Information

Course coordinators: