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| Module Availability |
Autumn/Spring |
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| Assessment Pattern |
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Coursework
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60%
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1.5 hour closed-book examination
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40%
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Qualifying Condition(s)
A weighted aggregate mark of 50% is required to pass this module.
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| Module Overview |
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| Prerequisites/Co-requisites |
MS103 Linear Algebra
MS205 Groups & Symetry
MS209 Algebra |
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| Module Aims |
This module develops students’ appreciation of algebraic structure through a study of Lie algebras and their matrix representations. |
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| 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. |
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| Module Content |
Lie algebras
subalgebras
ideals
quotient algebras
Derivations
homomorphisms.
Matrix representation of the Lie algebra sl2 and other standard examples.
Nilpotency, solvability and semisimplicity.
Engel’s Theorem
Lie’s Theorem.
The Killing form.
Cartan’s criteria
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| Methods of Teaching/Learning |
Teaching is by discussion and directed reading. Learning takes place through tutorials, directed reading, exercises and tests.
1 or 2 contact hours per week for 10 weeks plus directed reading.
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| Selected Texts/Journals |
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J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer
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| Last Updated |
30 July 2007 |
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