Álgebras de Loop e Cohomologia Galoisiana

Abstract

In this work we study how certain types of loop algebras can be classi ed with the help of Galois cohomology. In the rst part of the paper we expose the theory of nitedimensional Lie algebras and introduce the notion of a loop algebra. Subsequently we explain the relationship of loop algebras with the S=R-forms of g(R), where R is the ring of Laurent polynomials in one variable over an algebraically closed eld and S an extension of the ring. In the second chapter the theory of Galois cohomology will be developped. Finally we will show how isomorphism classes of loop algebras can be represented by elements of sets of Galois cohomology.