Valid from: Autumn 2013
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-01-27
Course type: Third-cycle course
Teaching language: English
The course is established to give a preparation for research within the theory of Lie algebras and groups; geometric mechanics; and theoretical physics.
Knowledge and Understanding
For a passing grade the doctoral student must be able to reproduce key results and sketch their proofs.
Competences and Skills
For a passing grade the doctoral student must
Basic definitions and examples. Structure theory of Lie Algebras. Correspondence between Lie Groups and Lie Algebras. Universal enveloping algebra. Semisimple Lie Algebras. Solvable and Nilpotent Lie Algebras. Root systems. Representations. Theory of highest weights.
One of the books is used, possibly with complementary hand-outs.
Types of instruction: Lectures, exercises
Examination formats: Written exam, oral exam
Grading scale: Failed, pass
Assumed prior knowledge: FMAF05 Systems and transforms and FMA200 Algebraic structures, or the corresponding knowledge.
The course will be given if there are at least six applicants.