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.

Bartolone, C., Di Bartolo A, Falcone G (2011). Nilpotent Lie algebras with 2-dimensional commutator ideals. LINEAR ALGEBRA AND ITS APPLICATIONS, 434(3), 650-656 [doi:10.1016/j.laa.2010.09.036].

Nilpotent Lie algebras with 2-dimensional commutator ideals

BARTOLONE, Claudio;DI BARTOLO, Alfonso;FALCONE, Giovanni
2011-01-01

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.
2011
Settore MAT/03 - Geometria
Bartolone, C., Di Bartolo A, Falcone G (2011). Nilpotent Lie algebras with 2-dimensional commutator ideals. LINEAR ALGEBRA AND ITS APPLICATIONS, 434(3), 650-656 [doi:10.1016/j.laa.2010.09.036].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/51845
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