250088 SE Infinite-dimensional Lie algebras (2014W)

The purpose of the seminar is to introduce and study certain infinite-dimensional Lie algebras (as well as aspects of their representation theory) which are relevant in conformal field theory, string theory, and for knot invariants. The first few sessions will review/introduce notions and results from the theory of finite-dimensional semi-simple complex Lie algebras. Then we move on to the Virasoro algebra Vir and its minimal representations; supersymmetric extensions of Vir; affine Kac-Moody algebras; Sugawara construction of Vir-representations. Further topics may include quantum groups and the basics of their 2-representation theory.