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Journal of Lie Theory 17 (2007), No. 1, 041--061
Copyright Heldermann Verlag 2007

Nilpotent Metric Lie Algebras of Small Dimension

Ines Kath
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22-26, 04103 Leipzig, Germany

In a recent paper [Transf. Groups 11 (2006) 87--131] 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 L with dim [L, L] = 2 which are used in this scheme. Furthermore, we use the scheme to classify all nilpotent metric Lie algebras of dimension at most 10.

Keywords: Nilpotent Lie algebra, invariant quadratic form.

MSC: 17B30, 17B56

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