MATH427-12S2 (C) Semester Two 2012
Lie Groups and Lie Algebras

Description

Lie groups are an essential tool in many areas of mathematics and physics. They are often found as groups of symmetries of `nice' mathematical objects like geometries or dynamical systems. The most important Lie groups are finite-dimensional and occur as groups of matrices over real or complex numbers. For example, the group SO(3) of all rotations of Euclidean 3-space or its closely related groups SU(2) and Spin(3) are Lie groups. One is interested in their properties and how these groups can be realised in higher dimensions.

Every Lie group has an associated Lie algebra which is a very good linear approximation of the group. Many properties of the Lie group can be deduced from its Lie algebra.

This course gives an introduction to the basic theory of finite-dimensional Lie groups and their associated Lie algebras and linear representations.

Pre-requisites

For further information see Mathematics and Statistics.