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.
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.
