Classification and Identification of Lie Algebras
Code | Completion | Credits | Range |
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D02KILA | ZK | 2P+0C |
- Course guarantor:
- Lecturer:
- Tutor:
- Supervisor:
- Department of Physics
- Synopsis:
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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:
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[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:
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans: