Organiser: Mehran Seyedhosseini

In this seminar, we will learn about Lie algebras and their representation theory.  Besides its inherent beauty, representation theory appears as a useful tool in various areas of mathematics and physics. It is the study of actions of algebraic objects such as groups or algebras on vector spaces. As the title suggest, the algebriac object we are interested in here is a Lie algebra. However,  we will also talk about Lie groups and point out how the results discussed in this seminar help us understand their representation theory.

A detailed plan of the seminar and a list of talks will appear soon in Moodle. The rough plan is as follows:

After defining Lie algebras and related basic notions, we will introduce different types of Lie algebras (solvable, nilpotent and semisimple). We will then discuss Lie's and Engel's theorem and the representation theory of solvable Lie algebras. Then we turn our attention to the study of the representation theory of certain semisimple Lie algebras. This is followed by a discussion of the abstract theory of roots and weights and a classification of irreducible representations of semisimple Lie algebras.

The main sources we will use are "Introduction to Lie algebras and representation theory" by Humphreys and "Representation theory, a first course" by Fulton and Harris.

The seminar will take place Wednesdays 14:!5 - 15:45.

For more information visit the Moodle page.