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

2018/06/03 by Johari, Farangis, Niroomand, Peyman
#17B05 #17B30 (Primary) #17B99 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1806.00872

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 (1)/(3) n(n-2)(n-1)+3-s₂(L). Characterizing the structure of all nilpotent Lie algebras has been obtained for the case s₂(L)=0. This paper is devoted to the characterization of all nilpotent Lie algebras when 0≤ s₂(L)≤ 6. Moreover, we show that which of them are 2-capable.

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