Descent constructions for central extensions of infinite dimensional Lie algebras

The purpose of this thesis is to give a new construction for central extensions of certain classes of infinite dimensional Lie algebras which include multiloop Lie algebras as motivating examples. The key idea of this construction is to view multiloop Lie algebras as twisted forms. This perspective provides a beautiful bridge between infinite dimensional Lie theory and descent theory and is crucial to the construction contained in this thesis, where central extensions of twisted forms of split simple Lie algebras over rings are constructed by using descent theory. This descent construction gives new insight to solve important problems in the structure theory of infinite dimensional Lie algebras such as the structure of automorphism groups of extended affine Lie algebras and universal central extensions of multiloop Lie algebras.;There are four main results in this thesis. First, by studying the automorphism groups of infinite dimensional Lie algebras a full description of which automorphisms can be lifted to central extensions is given. Second, by using results from lifting automorphisms to central extensions and techniques in descent theory a new construction of central extensions is created for twisted forms given by faithfully flat descent. A good understanding of the centre is also provided. Third, the descent construction gives information about the structure of the automorphism groups of central extensions of twisted forms. Finally, a sufficient condition for the descent construction to be universal is given and the universal central extension of a multiloop Lie torus is obtained by the descent construction.