Restricted One-dimensional Central Extensions of Simple Restricted Lie Algebras

TL;DR

This paper classifies one-dimensional central extensions of all finite-dimensional simple restricted Lie algebras over fields with characteristic at least 5, expanding understanding of their structure in modular Lie theory.

Contribution

It provides a complete description of restricted one-dimensional central extensions for simple restricted Lie algebras in characteristic p ≥ 5, a previously unclassified area.

Findings

Complete classification of central extensions for the algebras studied

Identification of conditions under which extensions exist

New structural insights into simple restricted Lie algebras

Abstract

In this paper, we describe restricted one-dimensional central extensions of all finite dimensional simple restricted Lie algebras defined over fields of characteristic $p\ge 5$.