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Nilpotent metric Lie algebras of small dimension
In a previous paper (Kath, Olbrich, Math. Z.246, 2004) we developed a general classification scheme for metric Lie algebras, i.e. for finite-dimensional Lie algebras equipped with a non-degenerate invariant inner product. Here we determine all nilpotent Lie algebras $\frak l$ with $\dim \frak l'=2$ which are used in this scheme. Furthermore, we classify all nilpotent metric Lie algebras of dimension at most 10.