Structure of nilpotent Lie algebra by its multiplier

  title={Structure of nilpotent Lie algebra by its multiplier},
  author={Peyman Niroomand},
  journal={arXiv: Rings and Algebras},
  • P. Niroomand
  • Published 8 March 2010
  • Mathematics
  • arXiv: Rings and Algebras
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 $s(L)=2.$ 
1 Citations
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Let L be a non-abelian nilpotent Lie algebra of dimension n and $$s(L)=\frac{1}{2}(n-1)(n-2)+1- \dim {\mathcal {M}}(L)$$s(L)=12(n-1)(n-2)+1-dimM(L), where $${\mathcal {M}}(L)$$M(L) denotes the Schur


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For a nilpotent Lie algebra L of dimension n and dim (L 2) = m ≥ 1, we find the upper bound , where M(L) denotes the Schur multiplier of L. In case m = 1, the equality holds if and only if L ≅ H(1) ⊕
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ABSTRACT Let L be a nilpotent Lie algebra of dimension n and C be a central extension by an ideal M of maximal dimension such that M is contained in the intersection of the center and the derived
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A new bound is obtained for the function g(h), whose existence was proved by Ledermann & Neumann (1956), such that ph divides the order of the automorphism group of a finite group G, if pg(h) divides