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

  • Afsaneh Shamsaki
  • Peyman NiroomandEmail author
Article
  • 7 Downloads

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 \( s(L)=4 \).

Keywords

Schur multiplier Nilpotent Lie algebra Capable Lie algebra 

Mathematics Subject Classification

17B30 

Notes

Acknowledgements

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

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceDamghan UniversityDamghanIran

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