## 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.