On some embedding of recursively presented Lie algebras

TL;DR

This paper demonstrates that recursively presented Lie algebras over certain fields can be embedded into a more specifically defined class of recursively presented Lie algebras with relations of a particular form.

Contribution

It introduces a method to embed any recursively presented Lie algebra over a finite extension field into a recursively presented Lie algebra with relations of a simplified, standardized form.

Findings

Every recursively presented Lie algebra over a finite extension field can be embedded into a Lie algebra with relations of the form a+b=c.

The embedding preserves the recursive presentation structure.

The relations in the embedded algebra are expressed as equalities of words and linear relations among generators.

Abstract

In this paper we prove that every recursively presented Lie algebra over a field which is a finite extention of its simple subfield can be embedded in a recursively presented Lie algebra defined by relations which are equalities of (nonassociative) words of generators and a+b=c, where a,b,c are generators.