Subnormal subalgebras of Leibniz algebras

TL;DR

This paper extends key properties of subnormal subalgebras from Lie algebras to Leibniz algebras, demonstrating similar structural results and module behavior in the more general setting.

Contribution

It generalizes classical results about subnormal subalgebras and module composition factors from Lie algebras to Leibniz algebras.

Findings

Subnormal subalgebras in Leibniz algebras share properties with those in Lie algebras.

The nilpotent residual of a subnormal subalgebra in Leibniz algebras is an ideal.

Module composition factors behave similarly in Leibniz algebra representations.

Abstract

Zassenhaus has proved that if U is a subnormal subalgebra of a finite-dimensional Lie algebra L and V is a finite-dimensional irreducible L-module, then all U-module composition factors of V are isomorphic. Schenkman has proved that if U is a subnormal subalgebra of a finite-dimensional Lie algebra L, then the nilpotent residual of U is an ideal of L. These useful results generalise to Leibniz algebras.