Title: An Introduction to Lie Algebra Cohomology

Abstract:

In this talk, we will discuss how Lie algebra cohomology is used as a tool to study infinite dimensional Lie algebras and their representations. In particular, we will see how the first cohomology space is used to construct new representations from known irreducible representations and the second cohomology can classify central extensions of an algebra. If time allows, we will discuss how the second cohomology space can be used to simplify the classification of extensions with length three or more.