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
• K. 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 7 module students will be able to:
1 demonstrate systematic understanding of Matrix Lie Groups and Lie Algebras;
2 demonstrate the capability to solve complex problems using a very good 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 a range of concepts and principles in Matrix Lie Groups and Lie Algebras theory in loosely defined contexts, showing good judgment in the selection and
application of tools and techniques.
The intended generic learning outcomes.
On successfully completing the level 7 module students will be able to:
1 work competently and independently, be aware of their own strengths and understand when help is needed;
2 demonstrate a high level of capability in developing and evaluating logical arguments;
3 communicate arguments confidently with the effective and accurate conveyance of conclusions;
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 effective use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material effectively;
8 demonstrate an increased level of skill in numeracy and computation;
9 demonstrate the acquisition of the study skills needed for continuing professional development.
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