Content: The concept of continuous symmetry suggested by Sophus Lie had an enormous influence on many branches of mathematics and physics in the twentieth century. Created first as a tool in a small number of areas (e.g. PDEs) it developed into a separate theory which influences many areas of modern mathematics such as geometry, algebra, analysis, mechanics and the theory of elementary particles, to name a few.

In this module we shall introduce the classical examples of Lie groups and basic properties of the associated Lie algebra and exponential map.

Books:

The lectures will not follow any particular book and there are many in the Library to choose from. See section QA387. Some examples:

C. Chevalley, Theory of Lie Groups, Vol I, Princeton.

J.J. Duistermaat, J.A.C. Kölk, Lie Groups, Springer, 2000.

F.W. Warner, Foundations of Differentiable Manifolds and Lie Groups, (Graduate Texts in Mathematics), Springer, 1983.