Capable Lie algebras with the derived subalgebra of dimension two over an arbitrary field

Abstract

In this paper, we classify all capable nilpotent Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field. Moreover, the explicit structure of such Lie algebras of class 3 is given.

arXiv commentTo appear in Linear Multilinear Algebra

References in corpus (4)

• Six-dimensional nilpotent Lie algebras
• A note on the Schur multiplier of a nilpotent Lie algebra
• Capability of Nilpotent Lie algebras with small derived Subalgebra
• Structure of nilpotent Lie algebra by its multiplier

Cited by in corpus (6)

• Nilpotent Lie algebras having the Schur multiplier of maximum dimension
• Nilpotent Lie algebras of class $4$ with the derived subalgebra of dimension $3$
• Characterization of finite dimensional nilpotent Lie algebras by the dimension of their Schur multipliers, $s(L)=5$
• On characterizing nilpotent Lie algebra by their multiplier, $ s(L)=6, 7
• On the triple tensor product of nilpotent Lie algebras
• The capability and certain functors of some nilpotent Lie algebras of class two