Lie Groups and Lie Algebras

The course is taught every third year, if there are enough students, next time Spring 2016. If there are few students, there will be guided self-study.
The course gives a basic introduction to classical Lie groups with emphasis on matrix groups and special examples such as SU(2), SO(3), Lorentz- and Poincare-groups, their structure, Lie algebras and representations. Furthermore, applications of Lie-theory will be given by examples from geometry, differental equations, classical physics or quantum mechanics.

1. Knowledge
The course gives a basic introduction to classical Lie groups with emphasis on matrix groups and special examples such as SU(2), SO(3), Lorentz- and Poincare-groups, their structure, Lie algebras and representations. Furthermore, applications of Lie-theory will be given by examples from geometry, differential equations, classical physics or quantum mechanics.

2. Skills
The students should be learn the theory of Lie-groups and Lie algebra and also be able to apply their knowledge in various applications to geometry, differential equations, classical physics or quantum mechanics.

3. Competence
The students should be able to participate in scientific discussions and conduct high level researches involving Lie groups and Lie algebras and also participate in interdisciplinary projects involving Lie groups and Lie algebras to other mathematical disciplines and also in physics.

Lectures, possibly as a guided self-study. Exercises, homework and/or home project