Structure of nilpotent Lie algebra by its multiplier

Abstract

For a finite dimensional Lie algebra $L$, it is known that $s(L)=\f{1}{2}(n-1)(n-2)+1-\mathrm{dim} M(L)$ is non negative. Moreover, the structure of all finite nilpotent Lie algebras is characterized when $s(L)=0,1$ in \cite{ni,ni4}. In this paper, we intend to characterize all nilpotent Lie algebra while $s(L)=2.$

References in corpus (3)

• A note on the Schur multiplier of a nilpotent Lie algebra
• Structure of nilpotent Lie algebra by its multiplier
• Characterizing finite $p$-groups by their Schur multipliers

Cited by in corpus (21)

• Capability of Nilpotent Lie algebras with small derived Subalgebra
• Structure of nilpotent Lie algebra by its multiplier
• Capable Lie algebras with the derived subalgebra of dimension two over an arbitrary field
• Some properties on the tensor square of Lie algebras
• $2$- capability and $2$- nilpotent multiplier of finite dimensional nilpotent Lie algebras
• Estimations of the low dimensional homology of Lie algebras with large abelian ideals
• Some results on the Schur multiplier of nilpotent Lie algebras
• The Bogomolov multiplier of Lie algebras
• Certain functors of nilpotent Lie algebra with the derived subalgebra of dimension two
• Nilpotent Lie algebras of class $4$ with the derived subalgebra of dimension $3$
• The structure of nilpotent Lie algebras of class two with derived subalgebra of dimension two
• The Schur multiplier of an $n$-Lie superalgebra
• Capability of nilpotent Lie algebras of small dimension
• Characterization of finite dimensional nilpotent Lie algebras by the dimension of their Schur multipliers, $s(L)=5$
• On the Schur $\mathsf{Lie}$-multiplier and $\mathsf{Lie}$-covers of Leibniz $n$-algebras
• On characterizing nilpotent Lie algebra by their multiplier, $ s(L)=6, 7
• On the dimension of Schur multiplier of Lie algebras of maximal class
• The capability and certain functors of some nilpotent Lie algebras of class two
• Characterizing nilpotent Lie algebras rely on the dimension of their $2$-nilpotent multipliers
• On the triple tensor product of nilpotent Lie algebras
• Characterizing nilpotent Lie algebras that satisfy on converse of the Schur's theorem