Nilpotent Lie algebras having the Schur multiplier of maximum dimension

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.