The capability and certain functors of some nilpotent Lie algebras of class two

Abstract

Recently, the authors obtained the Schur multiplier, the non-abelian tensor square and the non-abelian exterior square of $d$-generator generalized Heisenberg Lie algebras of rank $\frac{1}{2}d(d-1).$ Here, we intend to obtain the same results for $d$-generator generalized Heisenberg Lie algebras of rank $t$ when $\frac{1}{2}d(d-1)-3\le t\le \frac{1}{2}d(d-1)-1.$ Then, as a result, we give similar consequences for a nilpotent Lie algebra $L$ of class two when $\dim (L/Z(L))=d,$ $\dim L^2=t$ such that $\frac{1}{2}d(d-1)-3\le t\le \frac{1}{2}d(d-1)-1.$

We added more results on some nilpotent Lie algebras of class 2, and rewrite the proof again

References in corpus (4)

• The structure, capability and the Schur multiplier of generalized Heisenberg Lie algebras
• Capable Lie algebras with the derived subalgebra of dimension two over an arbitrary field
• Certain functors of nilpotent Lie algebra with the derived subalgebra of dimension two
• Some results on the Schur multiplier of nilpotent Lie algebras