6533b852fe1ef96bd12aa310
RESEARCH PRODUCT
Nilpotent Lie algebras with 2-dimensional commutator ideals
A. Di BartoloGiovanni FalconeClaudio Bartolonesubject
Discrete mathematicsPure mathematicsCommutatorNumerical AnalysisAlgebra and Number TheoryNilpotent Lie algebras Pairs of alternating formsNon-associative algebraCartan subalgebraKilling formCentral seriesPairs of alternating formsAdjoint representation of a Lie algebraNilpotent Lie algebrasLie algebraDiscrete Mathematics and CombinatoricsSettore MAT/03 - GeometriaGeometry and TopologyNilpotent groupMathematicsdescription
Abstract We classify all (finitely dimensional) nilpotent Lie k -algebras h with 2-dimensional commutator ideals h ′ , extending a known result to the case where h ′ is non-central and k is an arbitrary field. It turns out that, while the structure of h depends on the field k if h ′ is central, it is independent of k if h ′ is non-central and is uniquely determined by the dimension of h . In the case where k is algebraically or real closed, we also list all nilpotent Lie k -algebras h with 2-dimensional central commutator ideals h ′ and dim k h ⩽ 11 .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-02-01 | Linear Algebra and its Applications |