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 . In this paper, in virtue of a recent bound of Rai, we give the structure of all nilpotent Lie algebras that attain this bound.

Mathematics Subject Classification (2010): Primary: 17B30; Secondary: 17B05, 17B99.