FMA095F

Tillfällig

Lie Algebras

6

Ren forskarutbildningskurs

7151 (Matematikcentrum (inst LTH) / Matematik (LTH))

 -01-27

FN1/Anders Gustafsson

Engelska

Vid tillräcklig efterfrågan

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.

Representations.

Theory of highest weights.

be able to reproduce key results and sketch their proofs.

be able to compare key results.

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

Föreläsningar

övningar

Skriftlig tentamen

Muntlig tentamen

Underkänd, godkänd

FMAF05 Systems and transforms and FMA200 Algebraic structures, or the corresponding knowledge.

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.

The course will be given if there are at least six applicants.

FMA095F

 -01-27

FN1/Anders Gustafsson