The Fundamental Modules of the Classical Lie Algebras

Abstract

The main objective of this Thesis is the construction of the fundamental modules of the classical Lie algebras. Weyl’s Theorem shows that if L is a semisimple Lie algebra, then any finite dimensional L−module is a direct sum of irreducible L−modules. Since the classical algebras are semisimple, we just need the irreducible modules in order to obtain the others. On the other hand, the fundamental modules give us every irreducible L− module and, therefore, every finite dimensional L−module.