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Lie Theory
| Credits | 8 credit points |
| Instructors | Moerdijk, I. (Universiteit Utrecht), Boer, A.L. (Universiteit Utrecht) |
| I.Moerdijk@math.uu.nl, A.L.Boer@math.uu.nl | |
| Aim | Introduction to the theory of Lie groups and Lie algebras. |
| Description | The theory of Lie groups describes symmetry in (differential) geometry and thus plays a central role in modern mathematics and theoretical physics. A Lie group is to a large extent determined by its infinitesimal counterpart, its so-called Lie algebra. In the course, we will present some of the basic theory of finite dimensional Lie groups and Lie algebras, and a little bit about their linear representations. A good impression of the subject can be obtained from the literature mentioned below. |
| Organization | The lectures will be preceded by a two week crash course in weeks 37 and 38, providing the necessary background in the language of smooth manifolds (see prerequisites below). The course on Lie groups proper will start in week 39. Each week, there will be 2 hours of lectures, and one hour in which students will have to present specific examples or solutions to exercises. |
| Examination | The requirements for the course consist in group work during the course (presentation of exercises, handing in of solutions to exercises), and a take-home exam at the end of the course. |
| Literature | To a large extent, the course will follow the lecture notes by E. van den Ban (2003 version), freely available at http://www.math.uu.nl/people/ban/lecnot.html . Good and inexpensive classics worth buying are the small books "Lectures on Lie Groups" by J.F. Adams and "Lie groups and Lie algebras" by J.-P. Serre. |
| Prerequisites | Basic aquaintance with the language of differentiable manifolds, tangent bundles, vector fields, differential forms, etc. (In week 37 and 38 we will provide the possiblity to refresh your knowledge of these things, see above.) |
| Remarks | The course also forms part of the MRI Master Class "Symplectic Geometry and Beyond", see http://www.math.uu.nl/people/crainic/mcsymplectic.html. (Information about the course can also be obtained from this site.) |