Characterization of finite dimensional nilpotent Lie algebras by the dimension of their Schur multipliers, $s(L)=5$

TL;DR

This paper characterizes the structure of non-abelian nilpotent Lie algebras with a Schur multiplier dimension parameter s(L)=5, extending previous classifications for s(L) up to 4.

Contribution

It provides a complete structural classification of all non-abelian nilpotent Lie algebras with s(L)=5, filling a gap in the existing literature.

Findings

Classified all non-abelian nilpotent Lie algebras with s(L)=5

Extended previous classifications for s(L) ≤ 4

Enhanced understanding of Schur multiplier dimensions in Lie algebra theory

Abstract

It is known that the dimension of the Schur multiplier of a non-abelian nilpotent Lie algebra $L$ of dimension $n$ is equal to $\frac{1}{2}(n-1)(n-2)+1-s(L)$ for some $ s(L)\geq0 $. The structure of all nilpotent Lie algebras has been given for $ s(L) \leq 4 $ in several papers. Here, we are going to give the structure of all non-abelian nilpotent Lie algebras for $s(L)=5$.