Completions of Lie Algebras

TL;DR

This paper studies the class of all completions of a rational Lie algebra over a characteristic zero field, exploring how these completions relate to the original algebra and their structural properties.

Contribution

It introduces and analyzes the concept of completions of rational Lie algebras, providing a framework for understanding their structure over fields of characteristic zero.

Findings

Characterization of completions of rational Lie algebras

Structural properties of these completions

Relationship between rational and field-extended Lie algebras

Abstract

A Lie algebra $K$ over a field of characteristic zero $E$ is called a completion of a rational Lie algebra $L$, if it contains $L$ as $\mathbb{Q}$-subalgebra and the $E$-span of $L$ is equal to $K$. The class of all completions of a rational Lie algebra is studied in this article.