Embedding of post-Lie algebras into postassociative algebras

TL;DR

This paper proves that post-Lie algebras can be embedded into their universal enveloping postassociative algebras using Groebner-Shirshov techniques, establishing a foundational algebraic embedding result.

Contribution

It introduces a method to embed post-Lie algebras into postassociative algebras, expanding the understanding of their algebraic structure.

Findings

Post-Lie algebras embed injectively into their universal enveloping postassociative algebras.

Application of Groebner-Shirshov technique to prove the embedding.

Establishment of a foundational algebraic embedding result.

Abstract

Applying Groebner-Shirshov technique, we prove that any post-Lie algebra injectively embeds into its universal enveloping postassociative algebra.