Introduction to Lie Groups (U03836)

? Credit Points : 10 ? SCQF Level : 11 ? Acronym : MAT-4-Lie

Course for final year students in Honours programmes in Mathematics.

Matrix groups: the general and spacial linear groups and subgroups preserving bilinear forms. The Lie algebra of a matrix group: the exponential map. Transformation groups: the group acting on itself and on its Lie algebra: the adjoint representation. Quaternions. Integration over compact groups and applications. Rudiments of representation theory of compact groups.

Entry Requirements

? Pre-requisites : MAT-3-Alg Recommended MAT-3-DGe and concurrently MAT-4-RTh.

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Semester 2 (Blocks 3-4)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
08/01/2008	10:00	11:00	Lecture Room 5326, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	10:00	10:50	KB
Lecture	Friday	10:00	10:50	KB

Summary of Intended Learning Outcomes

1. An understanding of matrix groups and their Lie algebras, as an application of linear algebra.
2. An understanding of transformation groups and the notion of invariance.
3. Familiarity with the basic facts about representation theory of compact matrix groups.
4. To gain an appreciation of the interplay between different areas of mathematics in the setting of matrix groups.