On characterizing nilpotent Lie algebra by their multiplier, $ s(L)=6, 7

TL;DR

This paper classifies non-abelian nilpotent Lie algebras based on their multiplier invariant s(L) for values 6 and 7, extending previous classifications for smaller values.

Contribution

It provides a complete classification of nilpotent Lie algebras with s(L)=6,7, filling a gap in the understanding of their structure based on the multiplier.

Findings

Classified all non-abelian nilpotent Lie algebras with s(L)=6.

Classified all non-abelian nilpotent Lie algebras with s(L)=7.

Extended the known structure results for s(L) beyond 5.

Abstract

Let $ L $ be an $ n $-dimensional non-abelian nilpotent Lie algebra and $ s(L)=\frac{1}{2}(n-1)(n-2)+1-\dim \mathcal{M}(L) $ where $ \mathcal{M}(L) $ is the Schur multiplier of a Lie algebra $ L. $ The structures of nilpotent Lie algebras $ L $ when $ s(L)\in \lbrace 0,1,2,3,4,5\rbrace $ are determined. In this paper, we classify all non-abelian nilpotent Lie algebras $ L $ when $ s(L)=6,7. $