Unit name | Lie groups, Lie algebras and their representations |
---|---|
Unit code | MATHM0012 |
Credit points | 10 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 1A (weeks 1 - 6) |
Unit director | Dr. Suramlishvili |
Open unit status | Not open |
Pre-requisites |
MATH11005 (Linear Algebra and Geometry), MATH11006 (Analysis 1), MATH11007 (Calculus 1), MATH 20901 (Multivariable calculus) (or equivalently, Calculus 2). Students will be expected to have attained a degree of mathematical maturity and facility at least to the standard of a beginning level 7 student. |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Lie groups and Lie algebras embody the mathematical theory of symmetry (specifically, continuous symmetry). A central discipline in its own right, the subject also cuts across many areas of mathematics and its applications, including geometry, partial differential equations, topology and quantum physics. This unit will concentrate on finite-dimensional semisimple Lie groups and Lie algebras and their representations, for which there exists a rather complete and self-contained theory. Applications will be discussed. Students will be expected to have attained a degree of mathematical maturity and facility at least to the standard of a beginning level 7 student.
The aims of this unit are to introduce the principal elements of semisimple Lie groups, Lie algebras and their representations, for which there is a relatively complete and self-contained theory. The course will develop conceptual understanding as well as facility with calculation. By treating semisimple Lie groups as sets of finite-dimensional matrices (the alternative, more abstract point of view is to treat them as differentiable manifolds), the unit will be made accessible to a students with a broad range of backgrounds.
Additional unit information can be found at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html
A student successfully completing this unit will be able to:
The unit will be delivered through lectures. Lecture notes will be provided. Problem sheets will be assigned and marked, and solutions distributed.
100% Examination.
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
Essential: Typset lecture notes will be provided.
Further:
H Georgi, Lie Algebras and Particle Physics, 2nd edition (1999)
K Erdmann and MJ Wildon, Introduction to Lie Algebras, Springer (2004)
B Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, Springer-Verlag (2004)
JJ Duistermaat and JAC Kolk, Lie groups, Springer-Verlag (2000)