Lie Groups and Lie Algebras I

This course is the first half of the year-long introductory graduate sequence 18.745/18.755 on Lie groups and Lie algebras. Topics include foundations of the theory of Lie groups and Lie algebras; theorems of Engel and Lie; the universal enveloping algebra, the Poincare-Birkhoff-Witt theorem; free Lie algebras; the Campbell-Hausdorff formula; classification and structure of finite dimensional complex simple Lie algebras; their finite dimensional representations; and the Weyl character formula.