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# CLAUDIO BARTOLONE

## Nilpotent Lie algebras with 2-dimensional commutator ideals

• Autori: Bartolone, C.; DI BARTOLO, A.; Falcone, G.
• Anno di pubblicazione: 2011
• Tipologia: Articolo in rivista (Articolo in rivista)

### 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 dimk h < 12.