Lattices of subalgebras of Leibniz algebras

TL;DR

This paper characterizes the lattice structure of subalgebras in one-generator Leibniz algebras and explores how lattice isomorphisms relate their Leibniz kernels, revealing structural invariants.

Contribution

It provides a detailed description of subalgebra lattices in one-generator Leibniz algebras and establishes conditions under which lattice isomorphisms preserve Leibniz kernels.

Findings

Lattice of subalgebras is explicitly described for one-generator Leibniz algebras.

Lattice isomorphisms generally map Leibniz kernels to each other, except in one special case.

Abstract

I describe the lattice of subalgebras of a one-generator Leibniz algebra. Using this, I show that, apart from one special case, a lattice isomorphism between Leibniz algebras L, L' maps the Leibniz kernel of L to that of L'.