On nilpotent Lie algebras of small breadth

TL;DR

This paper characterizes finite-dimensional nilpotent Lie algebras with small breadth (≤2), providing classifications and isomorphism classes, thereby advancing understanding of their structure.

Contribution

It offers a complete characterization and classification of nilpotent Lie algebras with breadth up to two, which was previously not fully understood.

Findings

Characterization of nilpotent Lie algebras with breadth ≤2

Determination of isomorphism classes of these algebras

Enhanced understanding of the structure of small-breadth nilpotent Lie algebras

Abstract

A Lie algebra $L$ is said to be of breadth $k$ if the maximal dimension of the images of left multiplication by elements of the algebra is $k$. In this paper we give characterization of finite dimensional nilpotent Lie algebras of breadth less than or equal to two. Furthermore, using these characterizations we determined the isomorphism classes of these algebras.