Abstract: The classification of finite dimensional simple Lie algebras over the complex field was completed over 100 years ago. The standard presentation of these algebras is as matrix algebras. In this talk we will consider how one might represent a finite dimensional Lie algebra as differential operators on Laurent polynomials, and consider the existence of "nice" representations of this type.

While this is intended to be a technical talk, much of it should be at least moderately intelligible to any student having a background including linear and abstract algebra, and calculus.