Breadth and characteristic sequence of nilpotent Lie algebras

TL;DR

This paper explores the relationship between the breadth and characteristic sequence invariants of nilpotent Lie algebras, advancing classification efforts especially for those with breadth 2 and beyond.

Contribution

It establishes a connection between breadth and characteristic sequence, completing classifications for breadth 2 and initiating analysis for higher breadths.

Findings

Complete classification of nilpotent Lie algebras with breadth 2.

Framework for analyzing Lie algebras with greater breadth.

Abstract

The notion of breadth of a nilpotent Lie algebra was introduced by B. Khuhirun, K.C. Misra and E. Stitzinger and used to approach problems of classification up to isomorphism. In the present paper, we study this invariant in terms of characteristic sequence, another invariant introduced by M. Goze and J.M. Ancochea-Bermudez. This permits to complete the determination of Lie algebras of breadth 2 and to begin the work for Lie algebras with breadth greater than 2.