MA453-15 Lie Algebras
Introductory description
Lie algebras are related to Lie groups, and both concepts have important applications to geometry and physics.
Module aims
The Lie algebras considered in this course will be finite dimensional vector spaces over endowed with a multiplication which is almost never associative (that is, the products (ab)c and a(bc) are different in general). A typical example is the n^2 -dimensional vector space of all n\times n complex matrices, with Lie product [A,B] defined as the commutator matrix [A,B]=AB-BA . The main aim of the course is to classify the building blocks of such algebras, namely the simple Lie algebras of finite dimension over.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
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Learning outcomes
By the end of the module, students should be able to:
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Indicative reading list
J.E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1979
T.O. Hawkes, Lie algebras, Notes available from Maths Dept.
N. Jacobson, Lie algebras, Dover, 1979
Subject specific skills
N/A
Transferable skills
Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.
Study time
| Type | Required |
|---|---|
| Lectures | 30 sessions of 1 hour (20%) |
| Tutorials | 9 sessions of 1 hour (6%) |
| Private study | 111 hours (74%) |
| Total | 150 hours |
Private study description
Review lectured material and work on set exercises.
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group B1
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination | 100% | No | |
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Assessment group R1
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination - Resit | 100% | No | |
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Feedback on assessment
Marked coursework and exam feedback.
Courses
This module is Optional for:
- Year 1 of TMAA-G1PE Master of Advanced Study in Mathematical Sciences
- Year 1 of TMAA-G1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
- Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
-
TMAA-G1PC Postgraduate Taught Mathematics (Diploma plus MSc)
- Year 1 of G1PC Mathematics (Diploma plus MSc)
- Year 2 of G1PC Mathematics (Diploma plus MSc)
This module is Core option list F for:
- Year 4 of UMAA-GV19 Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations
This module is Option list A for:
- Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
- Year 4 of USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
- Year 5 of USTA-G1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Option list B for:
- Year 1 of TMAA-G1PC Postgraduate Taught Mathematics (Diploma plus MSc)
- Year 4 of UCSA-G4G3 Undergraduate Discrete Mathematics
- Year 5 of UCSA-G4G4 Undergraduate Discrete Mathematics (with Intercalated Year)
This module is Option list C for:
-
UMAA-G105 Undergraduate Master of Mathematics (with Intercalated Year)
- Year 3 of G105 Mathematics (MMath) with Intercalated Year
- Year 4 of G105 Mathematics (MMath) with Intercalated Year
- Year 5 of G105 Mathematics (MMath) with Intercalated Year
-
UMAA-G103 Undergraduate Mathematics (MMath)
- Year 3 of G103 Mathematics (MMath)
- Year 4 of G103 Mathematics (MMath)
- Year 4 of UMAA-G107 Undergraduate Mathematics (MMath) with Study Abroad
-
UMAA-G106 Undergraduate Mathematics (MMath) with Study in Europe
- Year 3 of G106 Mathematics (MMath) with Study in Europe
- Year 4 of G106 Mathematics (MMath) with Study in Europe
This module is Option list E for:
- Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated