Lie Algebras in Physics 1.

Course description:
Symmetries and conservation laws, space-time symmetry groups, angular momentum, sl(2), further examples. Notions and general results from the theory of Lie algebras (from basic definitions to the Levi decomposition). Elements of linear representations (fundamental definitions, Schur lemmas). Structure theory and classification of finite dimensional, complex, semisimple Lie algebras. Real forms. Definition of Kac-Moody algebras, Dynkin diagrams of affine Lie algebras. Overview of Lie groups.

Recommended Texts:

• Fuchs J., Schweigert C.: Symmetries, Lie Algebras and Representations, CUP, Cambridge, 1997
• Humphreys J. E.: Introduction to Lie Algebras and Representation Theory, Springer, Berlin, 1972