MA453-15 Lie Algebras

Department: Warwick Mathematics Institute
Level: Undergraduate Level 4
Module leader: Adam Thomas
Credit value: 15
Module duration: 10 weeks
Assessment: Multiple
Study location: University of Warwick main campus, Coventry

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.

N/A

Learning outcomes

By the end of the module, students should be able to:

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
Answerbook Gold (24 page)

Assessment group R1

	Weighting	Study time	Eligible for self-certification
In-person Examination - Resit	100%		No
Answerbook Gold (24 page)

Feedback on assessment

Marked coursework and exam feedback.

Past exam papers for MA453

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)
Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

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)
Year 4 of USTA-G1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (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 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated