Subinvariance in Leibniz Algebras

TL;DR

This paper introduces and studies subinvariant subalgebras within Leibniz algebras, extending concepts from Lie algebra theory and demonstrating analogous properties.

Contribution

It defines subinvariant subalgebras for Leibniz algebras and establishes their properties, generalizing known results from Lie algebras.

Findings

Subinvariance concepts extend from Lie to Leibniz algebras.

Analogous properties of subinvariance are proven for Leibniz algebras.

The paper bridges a gap between Lie and Leibniz algebra theory.

Abstract

Leibniz algebras are certain generalizations of Lie algebras. Motivated by the concept of subinvariance in group theory, Schenkman studied properties of subinvariant subalgebras of a Lie algebra. In this paper we define subinvariant subalgebras of Leibniz algebras and study their properties. It is shown that the signature results on subinvariance in Lie algebras have analogs for Leibniz algebras.