\'Etale Descent of Derivations

TL;DR

This paper investigates how derivations of algebraic structures behave under étale descent, focusing on twisted forms of algebras over rings, with applications to associative and Lie algebras including multiloop algebras.

Contribution

It provides a framework for étale descent of derivations applicable to various classes of algebras, including extended affine Lie algebras.

Findings

Established descent criteria for derivations of twisted algebra forms

Applied results to multiloop algebras in extended affine Lie algebra construction

Unified approach for associative and Lie algebra derivations

Abstract

We study \'etale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, such as the multiloop algebras that appear in the construction of extended affine Lie algebras.