Descent constructions for central extensions of infinite dimensional Lie algebras

TL;DR

This paper employs Galois descent to construct and analyze central extensions of twisted forms of split simple Lie algebras over rings, with applications to Extended Affine Lie Algebras and automorphism groups.

Contribution

It introduces a Galois descent method for constructing central extensions of infinite-dimensional Lie algebras over rings, advancing understanding of their automorphism groups.

Findings

Construction of central extensions via Galois descent

Insights into automorphism group structures

Application to Extended Affine Lie Algebras

Abstract

We use Galois descent to construct central extensions of twisted forms of split simple Lie algebras over rings. These types of algebras arise naturally in the construction of Extended Affine Lie Algebras. The construction also gives information about the structure of the group of automorphisms of such algebras.