Embedding of pre-Lie algebras into preassociative algebras

TL;DR

This paper demonstrates that every pre-Lie algebra can be embedded into a universal preassociative algebra using Rota-Baxter operators and Groebner-Shirshov bases, establishing a foundational algebraic embedding result.

Contribution

It introduces a method to embed pre-Lie algebras into preassociative algebras via Rota-Baxter operators and Groebner-Shirshov bases, providing a new algebraic construction.

Findings

Pre-Lie algebras can be embedded into preassociative algebras.

The embedding is injective and universal.

Utilizes Rota-Baxter operators and Groebner-Shirshov bases.

Abstract

With the help of Rota-Baxter operators and the Groebner-Shirshov bases, we prove that any pre-Lie algebra injectively embeds into its universal enveloping preassociative algebra.