Faithful representations of Leibniz algebras

TL;DR

This paper proves that every Leibniz algebra of dimension n has a faithful module of dimension at most n+1, providing a bound on the size of faithful representations.

Contribution

It establishes a universal upper bound on the dimension of faithful modules for Leibniz algebras, extending representation theory results.

Findings

Existence of faithful modules of dimension ≤ n+1 for Leibniz algebras

Provides a bound that is tight for certain cases

Advances understanding of Leibniz algebra representations

Abstract

Let L be a Leibniz algebra of dimension n. I prove the existence of a faithful L-module of dimension less than or equal to n+1.