Metric Lie algebras with maximal isotropic centre
The authors are interested in the classification of metric Lie algebras, that is, of finite-dimension\-al real Lie algebras equipped with an invariant non-degenerate symmetric bilinear form. In the present paper they determine the isomorphism classes of a certain type of solvable metric Lie algebras. They show that every metric Lie algebra of this type is a two-fold extension associated with an orthogonal representation of an abelian Lie algebra. The equivalence classes of such extensions are described by a certain cohomology set. As an application they obtain a classification scheme for metric Lie algebras with maximal isotropic center and the classification of metric Lie algebras of index 2.
orthogonal representations of abelian Lie algebras
Lie algebras with maximal isotropic center
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