Álgebras de Kac-Moody afim não torcidas como extensão central de álgebras de loop

Abstract

In the 1960s, Victor G. Kac and Robert V. Moody, working independently, provided a generalization of finite semisimple Lie algebras by means of the so-called generalized Cartan matrix (GCM). Such Lie algebras, discovered by Kac and Moody, are called Kac-Moody algebras and are usually infinite-dimensional algebras. This dissertation is devoted to the study of non-twisted affine Kac-Moody algebras, more precisely, the main result of this work is to provide a concrete construction (realization) of these algebras by means of a loop algebra where the base algebra is a finite dimensional simple Lie algebra.