This module is not currently running in 2024 to 2025.
• Introduction to Matrix Lie Groups: Basic examples. Matrix groups GL(n), SL(n), SO(n), Sp(n).
• Representations of SU(2): Tensor product of representations, Clebsch-Gordan series for SU(2).
• The Lie algebra of a Lie group. The exponential map.
• Introduction to Lie algebras: The Lie algebras gl(n), sl(n), so(n), sp(n). Nilpotent, solvable and semi-simple Lie algebras. The adjoint action of a group on its Lie algebra, and of a Lie algebra on itself. Derivations.
• Representations of sl(2).
Total contact hours: 42
Private study hours: 108
Total study hours: 150
80% Examination, 20% Coursework
Erdmann and M. Wildon: Introduction to Lie algebras. Springer Undergraduate Mathematics Series. Springer-Verlag London, Ltd., London, 2006. x+251 pp. ISBN: 978-1-84628-040-5; 1-84628-040-0
B. Hall: Lie groups, Lie algebras, and representations. An elementary introduction. Second edition. Graduate Texts in Mathematics, 222. Springer, Cham, 2015. xiv+449 pp. ISBN: 978-3-319-13466-6; 978-3-319-13467-3
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes
On successfully completing the level 6 module students will be able to:
1 demonstrate systematic understanding of key aspects of Matrix Lie Groups and Lie Algebras;
2 demonstrate the capability to deploy established approaches accurately to analyse and solve problems using a reasonable level of skill in calculation and manipulation of
the material in the following areas: Matrix Lie groups, Lie algebras, representations of Lie groups and Lie algebras;
3 apply key aspects of Matrix Lie Groups and Lie Algebras theory in well-defined contexts, showing judgement in the selection and application of tools and techniques.
The intended generic learning outcomes.
On successfully completing the level 6 module students will be able to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make competent use of information technology skills such online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation;
9 demonstrate the acquisition of the study skills needed for continuing professional development.
University of Kent makes every effort to ensure that module information is accurate for the relevant academic session and to provide educational services as described. However, courses, services and other matters may be subject to change. Please read our full disclaimer.
