On Levi Decompositions in Finite and Infinite Dimensional Lie Algebras

Abstract: In this bachelor thesis we introduce Lie algebras, and use Lie algebra cohomology to prove Levi's theorem about splitting of finite dimensional Lie algebras. We then construct the Virasoro algebra, compute its low dimensional cohomology spaces, and use this to demonstrate why Levi's theorem does not hold in the infinite dimensional case.