HNN-extension of involutive multiplicative Hom-Lie algebras

TL;DR

This paper develops HNN-extensions for involutive Hom-Lie algebras and involutive Hom-associative algebras, and uses these to prove an embedding theorem leveraging the Poincaré-Birkhoff-Witt theorem.

Contribution

It introduces the construction of HNN-extensions for involutive Hom-algebras and applies this to establish an embedding theorem for involutive Hom-Lie algebras.

Findings

HNN-extensions for involutive Hom-algebras are constructed.

An embedding theorem for involutive Hom-Lie algebras is proved.

The Poincaré-Birkhoff-Witt theorem is utilized in the proof.

Abstract

The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie algebras is described. Then, as an application of HNN-extension, by using the validity of Poincar\'e-Birkhoff-Witt theorem for involutive Hom-Lie algebras, we provide an embedding theorem.