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

Abstract

From [Problem 1729, Groups of prime power order, Vol. 3], Berkovich et al. asked to obtain the Schur multiplier and the representation of a group $G$, when $G$ is a special $p$-group minimally generated by $d$ elements and $|G^{\prime }|=p^{\frac{1}{2}d(d-1)}$. Since there are analogies between groups and Lie algebras, we intend to give an answer to this question similarly for nilpotent Lie algebras. Furthermore, we give some results about the tensor square and the Schur multiplier of some nilpotent Lie algebras of class two.

Cited by in corpus (7)

• Nilpotent Lie algebras having the Schur multiplier of maximum dimension
• Capability of nilpotent Lie algebras of small dimension
• The structure of nilpotent Lie algebras of class two with derived subalgebra of dimension two
• Multipliers, Covers and Stem Extensions for Lie Superalgebras
• Characterizing nilpotent Lie algebras that satisfy on converse of the Schur's theorem
• On ${\mathrm{ID}}^{\ast }$-superderivations of Lie superalgebras
• The capability and certain functors of some nilpotent Lie algebras of class two