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arXiv · 1806.00872

Characterizing nilpotent Lie algebras rely on the dimension of their $2$-nilpotent multipliers

Farangis Johari·Peyman Niroomand
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Abstract

There are some results on nilpotent Lie algebras $ L $ investigate the structure of $ L $ rely on the study of its $2$-nilpotent multiplier. It is showed that the dimension of the $2$-nilpotent multiplier of $ L $ is equal to $ \frac{1}{3} n(n-2)(n-1)+3-s_2(L).$ Characterizing the structure of all nilpotent Lie algebras has been obtained for the case $ s_2(L)=0.$ This paper is devoted to the characterization of all nilpotent Lie algebras when $ 0\leq s_2(L)\leq 6.$ Moreover, we show that which of them are $2$-capable.

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Farangis Johari, Peyman Niroomand. 2018-06-03. Characterizing nilpotent Lie algebras rely on the dimension of their $2$-nilpotent multipliers. https://arxiv.org/abs/1806.00872

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