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| Module Availability |
Autumn |
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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: One or two take-home assignments and one class test
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25
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Examination: 2 hours, unseen
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75
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Qualifying Condition(s)
An overall aggregate mark of 50% for the module is required to pass the module.
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| Module Overview |
| This module develops students’ appreciation of algebraic structure through a study of Lie algebras and their matrix representations. |
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| Prerequisites/Co-requisites |
| MAT1016 Linear Algebra, MAT2005 Algebra and Codes, MAT2006 Groups and Symmetry. |
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| Module Aims |
| The module aims to enhance students' appreciation of abstract algebraic structure theory. |
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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 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. |
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| 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. |
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| 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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| Last Updated |
| 27/05/10 |
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