The aim of the course is to provide the students with the knowledge of basic definitions and techniques in the classical theory of Lie Algebras, in order to enable him/her to understand and apply more recent results and developments (e. g., the ones about Kac-Moody and Virasoro-type algebras) to problems of Mathematical and Theoretical Physics.
Program
1) Nilpotent, Solvable, Semisimple Lie Algebras.
2) Root systems, Weyl Groups and their properties.
3) Cartan matrices and Dynkin diagrams.
4) Elements of the theory of highest weight modules.
The subjects listed above are extremely classical and can be found on any ``recent'' monography on Lie Algebras. For instance:
1) N. Jacobson, Lie Algebras.
2) J. E. Humphreys, Introduction to Lie Algebras and Representation Theory.
3) H. Samelson, Notes on Lie Algebras.
4) J.P. Serre, Complex Semisimple Lie Algebras.