Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FMA095F valid from Autumn 2013

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  • English
  • If sufficient demand
  • The course is established to give a preparation for research within the theory of Lie algebras and groups; geometric mechanics; and theoretical physics.
  • 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.


    Theory of highest weights.
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
  • be able to compare key results.

    be able to apply the basic techniques, results and concepts of the course to concrete examples and exercises.

Judgement and Approach
  • For a passing grade the doctoral student must
Types of Instruction
  • Lectures
  • Exercises
Examination Formats
  • Written exam
  • Oral exam
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • FMAF05 Systems and transforms and FMA200 Algebraic structures, or the corresponding knowledge.
Selection Criteria
  • Humphreys, J. E.: Introduction to Lie Algebras and Representation Theory. Springer, 1978. ISBN 0387900535.
    Kaplansky: Lie algebras and locally compact groups. 1995. ISBN 9780226424538.
  • One of the books is used, possibly with complementary hand-outs.
Further Information
  • The course will be given if there are at least six applicants.
Course code
  • FMA095F
Administrative Information
  •  -01-27
  • FN1/Anders Gustafsson

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