Duration
30h Th, 10h Pr, 20h Mon. WS
Number of credits
| Master in mathematics (120 ECTS) | 8 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
We will study finite dimensional Lie algebras, and focus on the main themes of the theory :
- classical constructions of Lie algebras : subalgebras, product, ideals, quotients;
- some important classes of algebras : nilpotent, solvable, simple and semi simple algebras;
- the classification of simple complex Lie algebras;
- some topics in the representation theory of complex Lie algebras.
Learning outcomes of the learning unit
The main learning outcome is obviously the knowledge of the theory of Lie algebras. But the students will also review the results of the first year course in algebra (linear algebra) and use them in various situations.
Prerequisite knowledge and skills
The first year lectures in linear algebra is mandatory to follow this series of lectures. A course in differential geometry would be helpful for the concrete examples it provides, but is not mandatory.
Planned learning activities and teaching methods
The lectures are given ex cathedra but students are encouraged to discuss with the teacher and ask questions.
Exercises will be proposed and discussed in the exercises sessions.
A personal work can be assigned to the students.
Mode of delivery (face to face, distance learning, hybrid learning)
Blended learning
Additional information:
It is a hybrid mode.
Recommended or required readings
Numerous books about Lie algebras are available at the library.
An important part of the final evaluation is the final exam concerning the theory.
Personnal work that can be assigned to the student can also be taken into account, as well as a potential written exam involving basic exercises and elemntary application of the theory.
Work placement(s)
Organisational remarks and main changes to the course
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Contacts
For theory and exercices, feel free to contact me by email :
P.Mathonet@uliege.be
to make an appointment or come to my office :
Department of Mathematics, Grande Traverse 12, B37, 4000 Liège Belgium. Office 0/27
You can also try to call me on the phone : +32(0)4/366.94.80