Characterizing nilpotent Lie algebras that satisfy on converse of the Schur's theorem

Abstract

Let $L$ be a finite dimensional nilpotent Lie algebra and $d$ be the minimal number generators for $L/Z(L).$ It is known that $\dim L/Z(L)=d\dim L^2-t(L)$ for an integer $t(L)\ge 0.$ In this paper, we classify all finite dimensional nilpotent Lie algebras $L$ when $t(L)\in \{0,1,2\}.$ We find also a construction, which shows that there exist Lie algebras of arbitrary $t(L).$

References in corpus (1)

• The structure, capability and the Schur multiplier of generalized Heisenberg Lie algebras