Course content

The course gives a basic introduction to Lie groups and their Lie algebras, mainly focusing on the case of matrix groups. Possible further topics include: representation theory (of semisimple Lie algebras or compact groups), algebraic structure theory of Lie algebras, geometry and topology of Lie groups.

Learning outcome

1. Knowledge. The student is able to articulate and explain the basic concepts and ideas behind Lie theory, and to elucidate their meaning using examples and application of algebraic or analytic nature.

2. Skills. The student has an overall understanding of Lie groups and Lie algebras. They can formulate problems and carry out simple calculations of Lie-theoretical nature, especially for matrix groups in lower dimensions.

Learning methods and activities

The learning methods and activities depend on the course teacher. The course will be given in autumn in years of even numbers.

Recommended previous knowledge

Basic analysis and group theory are required, as is a good knowledge of linear algebra. Some previous knowledge of topology is also an advantage.

Course materials

Information about course material will be given at the start of the course.