The theorems on freedom for relatively free Lie algebras with a relations

TL;DR

This paper proves theorems on the freedom of relatively free Lie algebras with a single relation and generalizes the Freiheitssatz, extending classical results to this algebraic context.

Contribution

It introduces new theorems on the freedom of relatively free Lie algebras with one relation and generalizes the Freiheitssatz for these algebras.

Findings

Proved the theorem on freedom for relatively free Lie algebras with a single relation.

Established a generalized Freiheitssatz for these algebras.

Extended classical algebraic results to the context of relatively free Lie algebras.

Abstract

In this paper we prove the theorem on freedom for relatively free Lie algebras with a single relation (analogous with the well-known result of Shirshov) and a generalized Freiheitssatz for relatively free Lie algebras (analogous with the well-known result of Kharlampovich).