Lattice isomorphisms of Leibniz algebras

TL;DR

This paper investigates how various algebraic properties of Leibniz algebras are preserved under lattice isomorphisms, contributing to the understanding of their structural invariants.

Contribution

It provides a detailed analysis of which properties like being Lie, simple, or nilpotent are invariant under lattice isomorphisms in Leibniz algebras.

Findings

Certain properties are preserved under lattice isomorphisms

Conditions like simplicity and nilpotency are invariant

The study clarifies structural invariants of Leibniz algebras

Abstract

Leibniz algebras are a non-anticommutative version of Lie algebras. They play an important role in different areas of mathematics and physics and have attracted much attention over the last thirty years. In this paper we investigate whether conditions such as being a Lie algebra, cyclic, simple, semisimple, solvable, supersolvable or nilpotent in such an algebra are preserved by lattice isomorphisms.