Lie Groups and Lie Algebras (LGLA | INK7020U)

Description: This course gives an introduction to the theory of Lie groups, Lie algebras and their representations. Lie groups are essentially groups consisting of matrices satisfying certain conditions (e.g. that the matrices should be invertible, or unitary, or orthogonal). They arise in many parts of mathematics and physics. One of the beauties of the subject is the way that methods from many different areas of mathematics (algebra, geometry, analysis) are all brought in at the same time. The course should enable you to go on to further topics in group theory, differential geometry, string theory and other areas.

Examples of Lie groups and Lie algebras in physics. Matrix Lie groups, matrix Lie
algebras, the exponential map, BCH formula. Abstract Lie algebras, examples: sl(2), sl(3), Poincare algebra. Representations of Lie algebras, sub-representations, Schur's Lemma, tensor products. Cartan-Weyl basis, classification of simple Lie algebras (without proof).

This module is taught at Kings College London.