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Lie algebras

Code: 61456
ECTS: 5.0
Lecturers in charge: doc. dr. sc. Slaven Kožić - Lectures
Lecturers: doc. dr. sc. Slaven Kožić - Exercises
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 15
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: The theory of Lie algebras is important in the group theory, mathematical physics, geometry and other mathematical theories. The aim of this course to introduce students with elements of the theory of Lie algebras and to present some methods and results in the representation theory of simple Lie algebras.

COURSE DESCRIPTION AND SYLLABUS:
1. Definition and examples of Lie algebras
2. Ideals, subalgebras and homomorphisms. Representations of Lie algebras.
3. Solvable and nilpotent Lie algebras. Engel's Theorem
4. Semisimple Lie algebras. Theorems of Lie and Cartan. Killing form.
5. Complete reducibility of representations. Weyl's theorem.
6. Representations of the Lie algebra sl(2,F)
7. Root space decomposition of a semisimple Lie algebra. Examples.
8. Root systems. Dynkin diagram.
9. Isomorphism and conjugacy theorems.
10. Universal enveloping algebra.
11. Finite dimensional representations of simple Lie algebras.
12. Highest weight representations. Verma modules.
13. Character formulas
Literature:
  1. J. E. Humphreys: Introduction to Lie algebras and representation theory
  2. N. Bourbaki: Lie groups and Lie algebras, Chapters 1 - 3
  3. N. Bourbaki: Lie groups and Lie algebras, Chapters 4 - 6
  4. R. Carter, G. Segal, I. Macdonald: Lectures on Lie groups and Lie algebras
  5. N. Jacobson: Lie Algebras
1. semester
Izborni predmet 1, 2 - Regular study - Theoretical Mathematics

2. semester
Izborni predmet 1, 2 - Regular study - Theoretical Mathematics

3. semester
Izborni predmet 3, 4 - Regular study - Theoretical Mathematics

4. semester
Izborni predmet 3, 4 - Regular study - Theoretical Mathematics
Consultations schedule: