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arXiv · 1812.00247

Nilpotent Lie algebras having the Schur multiplier of maximum dimension

A. Shamsaki·P. Niroomand
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Abstract

Let $ L $ be an $ n $-dimensional nilpotent Lie algebra of nilpotency class $ c $ with the derived subalgebra of dimension $ m $. Recently, Rai proved that the dimension of Schur multiplier of $ L $ is bounded by $ \frac{1}{2}(n-m-1)(n+m)-\sum\limits_{i=2}^ {min\lbrace n-m,c\rbrace} n-m-i $. In this paper, we obtain the structure of all nilpotent Lie algebras that attain this bound.

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A. Shamsaki, P. Niroomand. 2018-12-01. Nilpotent Lie algebras having the Schur multiplier of maximum dimension. https://doi.org/10.2989/16073606.2019.1606123

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