Derivations of certain algebras defined by \'etale descent

TL;DR

This paper explicitly describes the Lie algebra of derivations for a class of infinite-dimensional algebras obtained via étale descent, including multiloop algebras relevant to extended affine Lie algebras.

Contribution

It provides a new explicit characterization of derivations for twisted forms of central algebras constructed through étale descent.

Findings

Explicit description of derivation Lie algebras for certain infinite-dimensional algebras

Includes multiloop algebras used in extended affine Lie algebra construction

Advances understanding of algebraic structures via étale descent

Abstract

We give an explicit description of the Lie algebra of derivations for a class of infinite dimensional algebras which are given by \'etale descent. The algebras under consideration are twisted forms of central algebras over rings, and include the multiloop algebras that appear in the construction of extended affine Lie algebras.