Introduction to Lie Theory

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.

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.

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