Group and ring theory, as covered in basic algebra courses in the Bachelor Mathematics. See for instance in Sections I.1-5,7; II.1-3; III.1-6; IV.1-3; V.1,2,5 of

S. Lang, "Algebra", Graduate Text in Math. 211 (3rd edition), Springer,

or the Dutch syllabi "Algebra 1" (H.W.Lenstra, F.Oort) and "Ringen en lichamen" (H.W.Lenstra, F.Oort), which can be downloaded from

Knowledge of Lie groups and representation theory of finite groups is not necessary, but is helpful.

Aim of the course

A Lie algebra is a vector space endowed with a binary operation generalising the commutator bracket for associative algebras. Real and complex Lie algebras provide infinitesimal descriptions of smooth manifolds with compatible group structure (Lie groups). Semisimple Lie algebras form an important subclass of Lie algebras that abundantly appear in mathematical and physical contexts involving symmetries.

This course gives an introduction to the theory of semisimple Lie algebras and their representation theory. Topics covered in the course are: nilpotent and solvable Lie algebras, structure theory and classification of semisimple Lie algebras, universal enveloping algebras, representation theory of semisimple Lie algebras, and Chevalley groups.


Eric Opdam and Jasper Stokman