Affine Kac-Moody Groups as Twisted Loop Groups obtained by Galois Descent Considerations

TL;DR

This paper explicitly constructs affine Kac-Moody groups using Galois descent, providing generators, relations, and a realization as twisted loop groups, advancing understanding of their algebraic structure.

Contribution

It offers a new explicit presentation and realization of affine Kac-Moody groups through Galois descent, connecting them to twisted loop groups.

Findings

Explicit generators and relations for affine Kac-Moody groups

Realization of these groups as twisted loop groups

Application of Galois descent in their construction

Abstract

We provide explicit generators and relations for the affine Kac-Moody groups, as well as a realization of them as (twisted) loop groups by means of Galois descent considerations.