Paul Terwilliger, Spring 2018:

Introduction to Lie algebras

MWF 1:20--2:10

DESCRIPTION: 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.

Note: This course is normally called Math 747, but it is too late

to change the course number in the timetable.

Textbook: Roger Carter: Lie algebras of finite and affine type. Cambridge U. Press, 2005.

semester:

Spring

prereqs:

A good understanding of undergraduate linear algebra.