Math 522. Lie Groups and Lie Algebras I Instructor Syllabus
(1) A summary of the theory of finite group representations, including the symmetric group. Review of multilinear algebra.
(2) Linear Lie groups - definition and examples. Lie groups as manifolds.
(3) Lie algebras: As the tangent space at the identity to the Lie group, and also the definition as abstract objects. The exponential map. Examples, esp. sln, definition of simple Lie algebras.
(4) Representations of Lie groups and Lie algebras: Definition and some examples.
(5) Integration on groups, Peter-Weyl theorem.
Written by R. Kedem; approved by Robert Muncaster, August 24, 2005.