Universal central extensions of twisted forms of split simple Lie algebras over rings

TL;DR

This paper establishes conditions under which the descent construction yields the universal central extension of twisted forms of split simple Lie algebras over rings, including twisted multiloop Lie tori.

Contribution

It provides a general framework for identifying universal central extensions via descent, specifically for twisted forms of simple Lie algebras over rings.

Findings

Universal central extensions can be obtained through descent under certain conditions.

The method applies to twisted multiloop Lie tori.

Provides a unified approach for constructing universal central extensions.

Abstract

We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central extensions of twisted multiloop Lie tori are obtained by the descent construction.