Course overview
The course is an introduction to the theory of Lie groups and Lie algebras, concepts of fundamental importance in mathematics and theoretical physics. Lie groups encapsulate symmetries of diverse mathematical structures, for example differential equations and gauge theories. Lie algebras allow problems concerning symmetries to be treated by powerful algebraic methods. The course will focus on the relationship between a Lie group and its Lie algebra and on the classification of semi simple Lie algebras.
Course learning outcomes
- Demonstrate an understanding of the basic theory of Lie algebras and Lie groups and familiarity with a range of examples
- Demonstrate advanced skills in constructing rigorous mathematical arguments
- Apply the theory in the course to solve a variety of problems at an appropriate level of difficulty
- Demonstrate advanced skills in communicating mathematics