Capability of Nilpotent Lie algebras with small derived Subalgebra

Abstract

In this paper, we classify all capable nilpotent Lie algebras with derived subalgebra of dimension at most 1.

To appear in J. Algebra with new contributions of F.G. Russo

References in corpus (3)

• A note on the Schur multiplier of a nilpotent Lie algebra
• Structure of nilpotent Lie algebra by its multiplier
• Lie algebra F-normalisers are intravariant

Cited by in corpus (23)

• A description of pseudo-bosons in terms of nilpotent Lie algebras
• 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
• $2$- capability and $2$- nilpotent multiplier of finite dimensional nilpotent Lie algebras
• On the presence of families of pseudo-bosons in nilpotent Lie algebras of arbitrary corank
• $c$-nilpotent multiplier and $c$-capability of the direct sum of Lie algebras
• Certain functors of nilpotent Lie algebra with the derived subalgebra of dimension two
• Some results on the Schur multiplier of nilpotent Lie algebras
• Nilpotent Lie algebras having the Schur multiplier of maximum dimension
• Nilpotent Lie algebras of class $4$ with the derived subalgebra of dimension $3$
• Detecting Capable Lie Superalgebra
• Decomposition of the nonabelian tensor product of Lie algebras via the diagonal ideal
• Capability of nilpotent Lie algebras of small dimension
• The structure of nilpotent Lie algebras of class two with derived subalgebra of dimension two
• 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
• Capability and the Schur multiplier of generalized Heisenberg Lie superalgebras
• Characterizing nilpotent Lie algebras that satisfy on converse of the Schur's theorem
• The exterior product and homology of Hom-Lie algebras
• On the triple tensor product of nilpotent Lie algebras
• On the capablility of Hom-Lie algebras
• Characterizing nilpotent Lie algebras rely on the dimension of their $2$-nilpotent multipliers
• The capability and certain functors of some nilpotent Lie algebras of class two