Math 747: Lie Algebras

This course is an introduction to Lie algebras,
with a focus on semisimple Lie algebras over the complex numbers.
Topics will include: solvable and nilpotent Lie algebras,
Cartan subalgebras, the Cartan decomposition, the Killing form,
the root system, the Weyl group, Dynkin diagrams, Cartan matrices,
the PBW theorem, and Verma modules.

The lectures will be self contained and no prior knowledge of
the subject is assumed. This course should be valuable
to anyone interested in Lie theory, quantum groups,
algebraic combinatorics, number theory, and special functions.