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2010/1 Module Catalogue
 Module Code: MATM011 Module Title: LIE ALGEBRAS
Module Provider: Mathematics Short Name: MSM.LIE
Level: M Module Co-ordinator: FISHER D Dr (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
Module Availability


Assessment Pattern
 Unit(s) of Assessment
    Weighting Towards Module Mark( %)
Coursework: One or two take-home assignments and one class test
Examination: 2 hours, unseen
Qualifying Condition(s) 
An overall aggregate mark of 50% for the module is required to pass the module.
Module Overview
This module develops students’ appreciation of algebraic structure through a study of Lie algebras and their matrix representations.
MAT1016 Linear Algebra, MAT2005 Algebra and Codes, MAT2006 Groups and Symmetry.
Module Aims
The module aims to enhance students' appreciation of abstract algebraic structure theory.
Learning Outcomes

On completion our students should:


  • Know the definitions and properties of Lie algebras, subalgebras, ideals, homomorphisms and automorphisims;  


  • Be familiar with standard examples of Lie algebras and their representations by matrices;  


  • Understand the concepts of solvable, semisimple and simple Lie algebras, and know criteria for these properties;  


Be able to construct simple proofs similar to those met in the course.
Module Content

Lie algebras, subalgebras, ideals, quotient algebras


Derivations, homomorphisms and automorphisms of Lie algebras


Representations of Lie algebras.


Nilpotency, solvability and semisimplicity.  Engel’s Theorem. Lie’s Theorem.


The Killing form. Cartan’s criteria.   The Levi decomposition.
Methods of Teaching/Learning
Teaching is by lectures and tutorials: 3 hours per week for 11 weeks.  Learning takes place through lectures, tutorials, directed reading, exercises and class tests.
Selected Texts/Journals

K. Erdmann and M. Wildon, Introduction to Lie algebras, Springer



J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer
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