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On characterizing nilpotent Lie algebras by their multiplier, \(s(L)=4\)

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Abstract

Let L be a non-abelian nilpotent Lie algebra of dimension n and \(s(L)=\frac{1}{2}(n-1)(n-2)+1- \dim {\mathcal {M}}(L)\), where \({\mathcal {M}}(L)\) denotes the Schur multiplier of L. For a non-abelian nilpotent Lie algebra, we know \( s(L)\ge 0 \) and the structure of all nilpotent Lie algebras are well known for \( s(L) \in \lbrace 0,1,2,3 \rbrace \) in several papers. The current paper is devoted to obtain the structure of all nilpotent Lie algebras L, when \( s(L)=4 \).

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Acknowledgements

We would like to thank the referee for improving the readability of this paper.

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  1. School of Mathematics and Computer Science, Damghan University, Damghan, Iran

    Afsaneh Shamsaki & Peyman Niroomand

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  1. Afsaneh Shamsaki
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  2. Peyman Niroomand
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Correspondence to Peyman Niroomand.

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Shamsaki, A., Niroomand, P. On characterizing nilpotent Lie algebras by their multiplier, \(s(L)=4\). Rend. Circ. Mat. Palermo, II. Ser 69, 259–272 (2020). https://doi.org/10.1007/s12215-019-00402-7

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