Classification and Identification of Lie Algebras

Garant předmětu:

Libor Šnobl

Lecturer:

Libor Šnobl

Tutor:

Supervisor:

Department of Physics

Synopsis:

The aim of the course is to acquaint students with modern methods of study and identification of Lie algebras and to develop the necessary practical skills.

1) Summary of basic concepts of Lie algebras theory, structure of semi-simple complex Lie algebras

2) Invariants of coadjoint representation (a.k.a. Casimir invariants) and methods of their computation

3) Invariant characteristics of Lie algebras and their use in identification

4) Explicit decomposition of a given Lie algebra into the direct sum of algebras

5) Construction of Levi decomposition

6) Determination of nilradical

7) Structure of nilpotent Lie algebras

8) Solvable Lie algebras with given nilradical

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

[1] Libor Šnobl and Pavel Winternitz: Classification and Identification of Lie Algebras, AMS 2014

[2] K. Erdmann, M. J. Wildon: Introduction to Lie Algebras, Springer 2006

[3] S. Helgasson, Differential Geometry, Lie Groups, and Symmetric Spaces, AMS 2001

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans: