Projects and Assignments in Pure Mathematics
Lie algebras are key objects in many areas of modern mathematics and theoretical physics.
The aim of a 3MM project would be basic structure and classification theorem (including root systems); roughly corresponding to the first 4 chapters of Humphrey's book.
For a 4MM project some representation theory would be included.
Prerequisites:
A thorough understanding of level 2 linear algebra.
Books
Erdmann, Karin & Wildon, Mark: "Introduction to Lie Algebras", Springer, 2006.
Humphreys, James E.: "Introduction to Lie Algebras and Representation Theory", Springer 1978.
Fulton, William & Harris Joe: "Representation Theory, A First Course", Springer 1991
and many others
Pure projects homepage