An embedding theorem for Nijenhuis Lie algebras

TL;DR

This paper establishes an embedding theorem for Nijenhuis Lie algebras using HNN extensions and Gr"obner-Shirshov bases, demonstrating that every such algebra can be embedded into an extended algebra.

Contribution

It introduces the HNN extension for Nijenhuis Lie algebras and proves an embedding theorem using Gr"obner-Shirshov basis theory.

Findings

Every Nijenhuis Lie algebra embeds into its HNN-extension.

The use of Gr"obner-Shirshov basis provides a normal form for the construction.

The embedding theorem generalizes the understanding of Nijenhuis Lie algebras.

Abstract

This paper introduces the Higman-Neumann-Neumann extension (HNN extension; for short) for Nijenhuis Lie algebras and provides an embedding theorem. To this end, we employ the theory of Gr\"obner-Shirshov basis for Lie {\Omega}-algebras in order to find a normal form for our construction. Then we show that every Nijenhuis Lie algebra embeds into its HNN-extension. Nijenhuis Lie algebras, Gr\"obner-Shirshov basis, HNN extension