**Lecturer**: Prof. Vladimir S. Gerdjikov

**Annotation**: This doctoral level lecture course is intended to audience interested in theoretical physics and mathematics. Its purpose is to introduce the theory of semisimple Lie algebras so that the student could master their Cartan-Weyl basis, as well as to become familiar with important basic structures such as the root and weight systems, which are needed for constructing finite-dimensional irreducible representations. The final goal is the construction of the graded Lie algebras and the related Kac-Moody algebras. These are basic tools in contemporary theoretical and mathematical physics. They are fundamental tools for the infinite-dimensional completely integrable Hamiltonian systems and to a number of problems in quantum mechanics, statistical physics and others.

Course topics are found in this file.

**Place and time**: Institute of Mathematics and Informatics (BAS), hall 478.

**Schedule**:

First lecture – March 9th (Friday), 16:00, pdf;

Second lecture – March 16th (Friday), 16:30, pdf;

Third lecture – March 23rd (Friday), 16:30, video;

Fourth lecture – April 13th (Friday), 16:30, video**;**

**Fifth lecture – April 27th (Friday), 16:30;**

Quanterall and ABV Soft – presenting sponsors of IAPS lecture series in theoretical physics.

** LIVE STREAMING** of the lectures is planned on the IAPS YouTube channel.

**Referenced books**:

1. S. Helgason. Differential geometry, Lie groups and symmetric spaces. Academic Press, 1978.

2. M. Goto, F. Grosshans. Semisimple Lie algebras, Lecture Notes in Pure and Applied Mathematics vol 38 (M. Dekker Inc., New York and Basel 1978).

3. A.O. Barut and R. Raczka. Theory of Group Representations and Applications. (World Scientific, Singapore 1986).

4. Н. Бурбаки. Группы и алгебры Ли, главы 4-6, (Мир, Москва, 1972).

5. Н. Бурбаки. Группы и алгебры Ли, главы 7-8, (Мир, Москва, 1978).