Ado theorem for nilpotent Hom-Lie algebras

TL;DR

This paper extends the classical Ado theorem to a specific class of finite-dimensional nilpotent Hom-Lie algebras, demonstrating they admit faithful finite-dimensional representations.

Contribution

It introduces an Ado theorem analog for nilpotent Hom-Lie algebras, a novel result in the representation theory of Hom-Lie structures.

Findings

Existence of faithful finite-dimensional representations for the considered Hom-Lie algebras

Extension of classical Lie algebra results to Hom-Lie algebra context

New techniques for analyzing Hom-Lie algebra representations

Abstract

We prove an analog of the Ado theorem - the existence of a finite-dimensional faithful representation - for a certain kind of finite-dimensional nilpotent Hom-Lie algebras.