Embeddings in Lie algebras of subexponential growth

TL;DR

This paper proves that any countable-dimensional Lie algebra with subexponential growth can be embedded into a finitely generated Lie algebra with the same growth property, advancing understanding of algebraic embeddings.

Contribution

It introduces a method to embed locally subexponential growth Lie algebras into finitely generated ones, expanding the class of algebras known to have such embeddings.

Findings

Any countable-dimensional Lie algebra of subexponential growth can be embedded into a finitely generated Lie algebra of subexponential growth.

The embedding preserves the subexponential growth property.

The result applies over fields of characteristic not equal to 2.

Abstract

We prove that an arbitrary countable dimensional Lie algebra over a field of characteristic $\neq 2$ that is locally of subexponential growth is embeddable in a finitely generated Lie algebra of subexponential growth.