*Course Syllabus for*
# 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.

**Types of instruction:** Lectures, exercises

**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

**Course coordinators:**